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In This Chapter

^ Discovering the origins of Japanese medicine

^ Understanding disease according to Japanese medicine

^ Analysing your type

^ Exploring Japanese therapies and how they work ^ Finding a practitioner

Ou may be a bit surprised to find a whole chapter devoted to Japanese medicine. Unlike its counterparts – Chinese, Ayurvedic, and Tibetan medicine – it is less well known; in fact many people think of Japanese medicine as a copy of Chinese medicine. Yet this notion is far from the truth. The Japanese excel at amalgamating and refining ideas and in the field of traditional medicine they absorbed ideas from China, Korea, India, Persia, and Europe, added some authentic ideas and influences of their own, and came up with some genuinely original therapies that are now popular all over the world. Ever heard of shiatsu, macrobiotics, Zen, or Kanpo? These therapies all originated in Japan and in this chapter I introduce them to you and show you how they may be relevant to your health.

I must admit to some bias here, though. I had the pleasure of living, studying, and practising Asian medicine in Japan for five years and got to experience these Japanese therapies first hand and discovered just how beneficial they can be.

A (Very) Brief History of Japanese Medicine

Japanese medicine has its roots in the early native religion Shintoism, which is essentially a form of nature – and ancestor-worship that sees the world as inhabited by a myriad of deities and spirits. Neglect of these deities, or the influence of malevolent ones, was thought to be the root cause of disease and misfortune.

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In Japanese mythology, two deities, Izanagi and Izanami, are said to have given birth to the physical world and all natural phenomena, including water, wind, and plant life. They represent the male and female principles (like the YinAnd yangof traditional Chinese medicine we discuss in Chapter 4). According to legend, the deities

Gave birth to the Sun Goddess, Amaterasu. Amaterasu came to be regarded as the supreme Shinto deity and protector for the Japanese race and was revered by ordinary people who prayed to her for sun and rain for their crops and for their general health and well-being.

Ancient treatments therefore involved offerings and appeasement rituals to important deities, exorcism of malevolent spirits, and ritual cleansing and bathing to atone for misdeeds and to purify the body. Herbs also played a part in rituals and healing and were used for cleansing the body inside and out. Even the earliest texts mention plants and fruits such as Kuzu (arrowroot) and Momo (peach) that could be used for healing.

Fast forward to the fifth and sixth centuries AD when physicians and monks from Korea and China first visited Japan. They brought new medical ideas and practices, including acupuncture and moxibustion, and introduced Buddhism. Later, in the 16th and 17th centuries, European missionaries arrived bringing knowledge of surgical techniques and Western medical practices. For a while all these approaches existed side by side and institutes of medicine and divination were established that taught European medicine alongside traditional practices such as acupuncture and moxibustion (for more on these check out Chapter 9), herbal medicine (find more in Chapter 11), and rituals for exorcism – a set-up that would be quite remarkable even today!

But the warlords of Japan were jumpy about foreigners getting too much influence so, at several times in Japan’s history, they closed the doors to all outsiders. It is during these periods that Japanese medicine really came into its own as practitioners dived deep into their own resources and developed uniquely Japanese therapies.

Over the centuries these therapies have undergone constant development and innovation and now flourish in modern-day Japan, where traditional Japanese medicine and orthodox Western medicine exist quite comfortably side by side.

Deciphering Disease in Japanese Medicine

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In Japanese tradition, disease is seen as linked to the following: Impurity

Improper lifestyle

Disruption in the flow of Ki (vital energy) I Spiritual influences

The impurity idea dates right back to those ancient traditions where diseases, wounds, menstruation, sexual intercourse, and bad lifestyle habits were regarded as impurities that required cleansing. As a result, even today, bathing and purging are central aspects of therapy and in fact cleanliness and communal bathing, such as at the wonderful natural Onsen Spa baths throughout Japan, is a national pastime.

Improper lifestyle habits refer to activities that conflict with living in harmony with the laws of nature. These habits include dressing inappropriately for the season, staying up late and getting inadequate sleep, eating unseasonable foods or over-eating, over-working and taking insufficient rest, staying indoors for long periods of time, excessive smoking or drinking, and excessive sexual contact. It is believed that these habits cause imbalance in the body, mind, and spirit and eventually result in disease.

Disruption of the flow of Ki, Or vital energy, in the body (this concept is identical to that of Qi In Chinese medicine described in Chapter 4) is believed to be due to the influence of external pathogenic factors known as Ja-ki (literally, evil energy). These factors are thought to be able to enter the body and disrupt body processes leading to chronic, weak, deficiency (kyo) Conditions or acute, painful, excess (jitsu) Ones. Disruption may also be caused by improper diet, stress, injury, environment, or even mental state. At any given time, Ki Energy may become depleted in a certain part of the body giving rise to an empty, or Kyo State, while in another part of the body an accumulation or blockage of Ki May exist leading to an excess, or Jitsu Condition. Yet Kyo And Jitsu Co-exist with each other, just like Yin And Yang In Chinese medicine, and so in the body they represent a constantly changing state of balance within a unified whole.

Kyo And Jitsu Can be related to mental and emotional states and the fulfilment of needs and desires as well as to aspects of your physical body. So, for example, if you’re hungry, this is an

Empty or Kyo State with the desire or need for food. After you eat and become satiated, this is a Jitsu State relating to fullness and the fulfilment of your desire.

The body always strives to maintain a balance between Kyo And Jitsu And a healthy person usually succeeds in achieving this. However, if things get too far out of balance, then the body can no longer cope, which is where Japanese therapies can be utilised to restore equilibrium.

Spiritual influences are still taken into consideration in traditional medicine in modern-day Japan due to the widespread belief in karma and reincarnation. A belief in Karma Means accepting that every action you take, or every thought that you have, as well as your general conduct has an influence on your subsequent destiny, while a belief in reincarnation means believing in past and future lives.

Diseases are also thought to have a karmic cause, relating to a behaviour or experience in a past life. For such diseases it is believed that only spiritual remedies will help and therefore religious rituals, exorcism and prayer will be employed as therapy on the advice of priests or monks.

Understanding Your Health – the Japanese Way

In this section I show you how you can determine your own Kyo (deficient) or Jitsu (excess) balance by assessing yourself according to common characteristics associated with each. After you determine your basic type you can make simple changes to your diet, lifestyle, and daily habits to help restore balance in the body and improve your health.

Determining your type according to Japanese medicine

Go through both checklists in Table 7-1 answering yes or no to each of the questions. Then tally your totals for each checklist. The list with the most yes answers is your current type according to Japanese medicine.

Table 7-1 Figuring Out Your Type

CHECKLIST A Yes No

Do you often feel tired or exhausted? Do you feel the cold easily?

Do you suffer from mild aches or pains that feel better for warmth or pressure?

Are you generally pale?

Do you lack strength and muscle tone?

Do you often feel mentally slow and forgetful?

Do you often feel tired on waking?

TOTAL ‘YES’ _/7

CHECKLISTB

Do you often feel irritable and restless? Do you often feel hot?

Do you suffer from acute pain and/or red and swollen joints?

Do you experience stiffness and pain on pressure?

Are you generally flushed or red-faced?

Are you always on the go and constantly feeling hyped up?

Do you find it hard to get to sleep and/or experience wakefulness during the night?

TOTAL ‘YES’ _/7

Adopting self-care for your type

Now that you’ve added up your answers in each checklist and determined which type you scored most for, take a look at the descriptions below to see whether you’re predominantly a Kyo Or Jitsu Type and what self-care practices you can adopt to support your body balance.

Deficiency (kyo) type

If most of your ticks are in Checklist A, then you are predominantly a Kyo Type. This means that you tend to be deficient in energy and may suffer from cold conditions, general weakness, fatigue, and impaired mental function to a greater or lesser degree.

According to Japanese medicine, deficient types may find the following self-care tips helpful to boost general vitality and protect against the health problems associated with deficiency:

I Keep yourself warm at all times.

I Wrap up well, taking care to keep your midriff, lower back, and feet covered.

I Avoid walking barefoot on cold floors.

I Avoid getting wet or sitting for long periods in damp or wet clothes.

I Eat lots of warming and easily digestible foods such as soups, casseroles, and steamed vegetables.

I Add warming spices such as cinnamon and ginger to your food and drinks.

I Chew your food well.

Avoid intake of cold or iced foods and drinks.

I Avoid caffeine-based drinks such as coffee and colas and replace these with nourishing beverages such as dandelion coffee, ginseng tea, and ginger tea.

Make sure that you drink six to eight glasses of water daily. I Take some gentle exercise like walking every day. I Do not overtire yourself. I Get plenty of rest and sleep.

I Make sure you’re comfortable and warm at night. I Use ginger baths and compresses to warm your body. I Avoid anxiety and worry and take steps to reduce your stress.

Excess (jitsu) type

If most of your ticks are in Checklist B, then you are predominantly a Jitsu Type. This means that you tend to have an excess of energy in particular parts of the body and may suffer from hot conditions, digestive problems, painful and stiff joints, irascibility, and impatience to a greater or lesser degree.

According to Japanese medicine, excess types may find the following self-care tips helpful to calm and cool things down, remove blockages, and protect against the health problems associated with excess.

I Keep yourself cool and avoid sitting in direct sun or hot, stuffy rooms. I Wear clothing with thin layers of cotton or other natural fibres.

I Eat plenty of cooling foods such as salads and other raw foods. I Avoid excessively spicy or over-hot foods. I Avoid over-eating. I Chew your food well.

I Avoid stimulants such as caffeine, alcohol, and sugar and avoid any recreational drugs.

I Drink six to eight glasses of water daily.

I Avoid sitting in any one place for extended periods. Get up and move about.

I Take regular, vigorous exercise.

Practise deep breathing. I Build appropriate relaxation into your daily routine. I Work less, play more, and take regular breaks. I Get adequate rest and sleep.

I Take short baths in warm, not hot, water, and add pouches of grated Daikon (long white radish) and parsley to ease discomfort.

I Practise patience and tolerance.

Understanding Diagnosis in Japanese Medicine

Practitioners of Japanese medicine determine your Kyo And Jitsu And your overall health balance by means of four types of diagnosis (shin):

Palpation (Setsu-shin) Observation (Bo-shin) Listening and smelling (Bun-shin) Questioning (Mon-shin)

Diagnosis by palpation (Setsu-shin)

With Setsu-shin, The practitioner takes pulses on each of your wrists and may also palpate your abdomen and specific points along the meridian channels

(channels of vital energy in the body – see Chapter 4 for the lowdown on these). As in traditional Chinese medicine, Japanese medicine recognises six pulses on each wrist, corresponding mainly to each of the major organs of the body. (Go to Chapters 2 and 4 to find out more about pulse taking.) In Japanese medicine, pulse taking has a slightly lighter touch than in Chinese medicine and the practitioner generally takes the pulses on both of your wrists at the same time, comparing the left and right sides of each pulse position with each other.

Abdominal palpation may also be used to determine the relative Kyo And Jitsu Of all your internal organs. Master practitioner Shizuto Masunaga employed a unique form of Hara (abdominal) diagnosis. This same form is used by many shiatsu practitioners and some acupuncturists today.

The practitioner palpates each area feeling for fullness (jitsu) Or emptiness (kyo). A diagnosis for fullness occurs when the abdomen feels hard and often tender when pressed. In an emptiness diagnosis, the abdomen feels soft and fingers sink in without resistance.

Practitioners also often palpate along meridian lines. Again they are feeling for areas that are soft and sunken and that welcome pressure (kyo) Or those that are hard and resistant and painful on pressure (jitsu). These points will form the basis of treatment in both Japanese acupuncture and massage, including Shiatsu.

Diagnosis by observation (Bo-shin)

Bo-shin Involves looking at the tongue and sometimes also the fingers, toes, ears, and face. The Japanese medicine practitioner examines the tongue to assess its colour, shape, and coating for information about the functioning of your internal organs (go to Chapter 2 for more details on tongue and face signs and what they can tell you about your health).

Micro-diagnosis, which involves the examination of an individual body part for information about the whole body, is also a speciality in Japanese medicine. Just as different parts of the tongue are said to correspond to various parts of the body, so too it is said to be possible to examine the hands, fingers, toes, face, ears, and so on for similar clues.

For example, in analysing the fingers and toes, redness, red spots, and the sensation of heat in a particular digit indicate a Jitsu (excess) condition in the organ to which it corresponds, while pallor, white or brown spots, or sensations of coldness can indicate Kyo (deficiency).

The practitioner may also take note of your gait, body size and proportions, skin, nails, hair, facial expressions, and even the colour of clothes that you’re wearing as all can provide valuable clues to your current state of health.

Diagnosis by listening and smelling (Bun-shin)

Bun-shin Diagnosis includes listening to the quality of your voice (loud, quiet, soft, grating, and so on), the sound of your breath (wheezy, rasping, noisy, quiet, and so on), and any gurgling sounds in the intestines that can indicate digestive problems or areas of blockage. A Bun-shin Diagnosis also notices any type of body odour (bitter, pungent, sweet, and so on) or bad breath. In questioning, you are also likely to be asked about any type of odour associated with your urine and stools because this can also provide useful diagnostic information.

Diagnosis by questioning (Mon-shin)

Your Japanese medical practitioner is likely to ask you about everything from your taste in food, to your bowel and sleep habits, as well as the usual details of your symptoms and medical history. However, as with traditional Chinese medicine (TCM), some practitioners do not speak or ask you much at all, preferring to focus on observation and palpation to see what the body can communicate directly.

The body may reveal secrets you yourself are not yet aware of, such as signs of stress damage, even though you may be thinking that you are coping just fine, or early warning distress signs from a particular organ that you are cheerfully abusing, such as the lungs in smokers or the spleen and stomach in people who eat loads of sweets.

The four forms of diagnosis used in Japanese medicine are all closely linked to the correspondences of the Five Elements. Whiz over to Chapter 4 to see a full table outlining what these are and showing how you can make links, for example, between shouting and liver function, yellow skin and stomach function, and salty taste and the kidneys.

Once the Japanese practitioner has used these diagnostic skills to assess your health balance, then, with your practitioner, you can decide what form of treatment is the most suitable for you.

Restoring Balance with Japanese Therapies

Japanese therapies aim to purify, cleanse, and balance the body by expelling the pathogenic Ja-ki (evil energy), balancing Kyo And Jitsu, And normalising the flow of Ki Vital energy and bodily functions. The overriding aim is to bring the body back into harmony with itself and back in tune with the cycles of the natural world.

The most widely used therapies are the following:

I Japanese acupuncture and moxibustion (warming therapy) I Kanpo (herbal medicine)

I Japanese massage techniques (including Shiatsu And Anma) I Ampuku (abdominal massage and therapy)

I Japanese manipulation techniques (including Honetsugi (bone-setting) and So-tai (a gentle manipulation therapy))

I Cleansing hydrotherapies (onsen Spa baths)

Dietary therapy (using certain foods for their medicinal effects or following therapeutic diets)

Japanese meditation practices such as Zen

I Spiritual medicine (prayer offerings, religious rituals, pilgrimages, and the like)

Alongside these therapies, practitioners are likely to give you a myriad of self-care recommendations related to your daily lifestyle (such as the ones mentioned in the section ‘Adopting self-care for your type’, earlier in this chapter).

Japanese acupuncture and moxibustion (warming therapy)

Japanese acupuncture is similar to the acupuncture practised in traditional Chinese medicine (TCM), but the needles are finer and the techniques more delicate and varied.

Insertion is generally painless and shallow. Sometimes the needle is just held against the skin without actually being inserted, or the skin is stimulated by the blunt edge of a small metal instrument. Fine metal rollers are also used to stimulate the meridian channels, especially in the treatment of children.

The selection of points is also a little different. Many different styles exist but in general fewer points are selected than in TCM and more use is made of the extraordinary meridians. (To read more about meridians and Japanese acupuncture, have a read of Chapters 4 and 9.)

The use of Ring needles, Which are worn for extended periods (also described in more detail in Chapter 9), is very popular as are tiny little magnets on plasters that can be worn for several days to stimulate circulation and ease pain.

Japanese acupuncturists also use a range of other associated techniques, which we discuss in the following sections.

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Moxibustion

Moxibustion (also known as moxa) is a warming treatment that involves burning an aromatic herb, Artemesia Vulgaris, To increase circulation and stimulate the flow of Ki (vital energy). In Japan, moxa applied directly to the skin is favoured, so fine moxa wool (the dried herb) is gently hand-rolled into tiny rice-grain-sized pieces and then placed directly on the skin, lit with a fine incense stick, and burnt down. The whole process is repeated several times on the same spot until the surrounding skin becomes red and warm.

During my Asian medical training in Japan, I spent many hours practising this technique, rolling the fine moxa wool into minute sausage shapes between the thumb and forefinger. Being speedy is handy when you have to repeat the treatment many times on various acupoints, often simultaneously. One of my teachers, Kitaoka-sensei, once demonstrated his swiftness across a set of six pairs of points on someone’s back. With lightning speed he placed the moxa grains, lit them, put them out, and replaced them all in quick succession; by the time he got to the bottom pair on the lower back he was just in time to go back to the top pair by the neck as they burnt down and extinguished themselves. Watching him execute this skill was mesmerising, rather like watching an expert juggler in a circus!

The idea of the rice grain moxa is that it is used to warm and tonify the body when a person has a deficient (kyo) Condition. The grains are placed repeatedly on the same point until the person starts to feel a sensation of heat. In Japanese medicine, since the moxa grains are so tiny, they are often allowed to burn right down to the skin. Doing so can produce tiny burn marks or

Blisters but is believed to be therapeutic by mobilising immune cell function. Actually, the marks disappear within a few days, leaving the skin unblemished.

In most people heat is felt after three to five moxa applications as the empty point becomes filled, but in some cases it can take much longer.

Cupping

Cupping is sometimes practised in Japanese medicine with round glass cups shaped like glass balls, which have an opening at one end. A lighted taper is placed inside to heat up the air inside the cup, which is then quickly placed on the skin. This process creates a vacuum, drawing up the skin into a bulge inside the cup and holding the cup in place. The effect is to stimulate circulation and the whole procedure is only mildly uncomfortable. However, cupping does leave small, red/purple rings on the skin, most famously seen on film star Gwyneth Paltrow’s back, but these fade within a few days. The technique is particularly popular amongst elderly Japanese women with back pain, office workers with neck and shoulder pain, and young women with menstrual problems.

Blood-letting

Blood-letting involves a small incision being made in the skin with a fine three-edged needle and the removal of a few drops of blood. Usually this technique is used on the fingertips to relieve fever or on the upper back to relieve neck and shoulder pain. Blood-letting can be combined with cupping, and surgical gloves are used to prevent blood contact. The technique is used -fcOOTf To remove blood stagnation and encourage fresh blood circulation.

The most moxa applications I have ever had to emergency acupoint, used for alcohol poison-do was in the case of a young friend who had ing, on the sole of the foot, taking one foot each been disappointed in love and turned up at my and working in tandem. Almost one hour later, Tokyo apartment just past midnight. He’d been after nearly 100 applications to the same point on a bender, combining beer with huge amounts the friend suddenly stirred, murmured some-of Japanese whiskey and was in a terrible state. thing about feeling heat on his foot and then He staggered through the door, wailed some- rolled over and slept soundly on the floor until thing about his lost love, and then promptly the next morning. When he awoke he, remark-passed out on the floor in a drunken stupor. I ably, had no hangover and simply got up and was unable to rouse him in any way. He was out went off to work. The moxa seemed to have cold and I was quite concerned. My partner, an restored him but they were unable to cure his acupuncturist, suggested moxa treatment and broken heart! together we began lighting moxa grains on an

Kanpo

The term Kanpo, Meaning ‘the way of Han’, is taken from an ancient Chinese herbal text called Shang Han Lun, Written by a doctor, Zhang Zhong Jing, almost 2,000 years ago. Zhang has been nicknamed the Chinese Hippocrates because his prescriptions, herbal formulae, acupuncture, and lifestyle recommendations are still in use today.

Zhang is famous for having said, ‘Even though doctors are not able to cure all diseases, they

Can discover the course of diseases by using certain theories, and guide themselves to treatment principles. If my book can help doctors do that, it would overwhelmingly satisfy my expectations by more than 50 per cent.’ This humble sentiment has been more than met and we wonder how he would have felt if he’d known his ideas would endure for almost two millennia, inspiring countless practitioners and undoubtedly helping countless patients to this day.

Magnet therapy

Magnet therapy is very popular in Japan, with millions of tiny magnets on plasters being sold over the counter in pharmacies each year. These plasters are also quite widely used by Japanese acupuncturists, who place them on areas of stiffness and pain, to bring relief, or on acupoints, to balance the flow of energy within the meridian channels.

Kanpo (herbal medicine)

The Japanese herbal medicine tradition developed originally from Chinese texts but, like many of the therapies described earlier in this chapter, went through uniquely Japanese stages of refinement and development. Nowadays, in Japan, only medical doctors are legally allowed to practise Kanpo, Yet over the counter Kanpo Remedies for the general public are hugely popular.

Japanese formulae generally use fewer herbs than the Chinese ones and dried granular extracts are more commonly used than fresh herbal ingredients because they’re convenient and easy to take.

Kanpo Diagnosis is based on eight principles described below as four pairs of opposites:

I Determining if the person’s symptoms are predominantly Kyo (deficient) or Jitsu (excess)

I Determining the stage of illness (chronic/acute)

Ascertaining whether the disease is external and superficial or internal and deep

Determining whether symptoms are predominantly hot or cold

The relative balance of the eight principles is diagnosed using the four methods of diagnosis described earlier in this chapter (palpation, including abdominal diagnosis; observation; listening and smelling; and questioning).

After the predominant underlying weakness, or Kyo, Has been identified, it can then be treated with appropriate medicinal herbs. This approach is almost the opposite to the Western medical one, which focuses on identifying and treating the invading germ, virus, or bacteria. In Kanpo, The emphasis is on supporting the weak or vulnerable parts or systems of the body to prevent them from succumbing to invading pathogens.

Because Kanpo Medicine focuses on an individual’s constitution and that person’s particular response to the disease, the treatment for different people with the same disease, according to Western medicine, will often be different. So, for example, if five people were diagnosed with asthma, in Western medicine they may all be prescribed the same type of inhalant medication, yet, in Kanpo, Their herbal medicine prescriptions, while maybe having some ingredients in common, would probably all differ.

Most Kanpo Formulae have five to ten ingredients. They’re usually made from plant ingredients including roots, bark, leaves, flowers, fruit, and fungi, although occasionally mineral or animal ingredients may be used. These ingredients are selected according to their individual effects on the body and also their combined effects with each other.

Kanpo Herbal medicines are well researched and are regarded as safe to take, with virtually no side effects if prescribed and taken properly.

If you’re pregnant, breast-feeding, or hoping to conceive you must always inform your practitioner or consult your GP before taking Kanpo Medicinal herbs.

You can take Kanpo Herbal medicines with Western medicine but ensure you’re carefully monitored by qualified and experienced practitioners in case of interactions. Always inform your GP and herbal practitioner of any medicines and herbs that you’re taking.

Japanese massage techniques (including shiatsu and anma)

Anma, shiatsu, And Western massage are the three most commonly practised types of massage in Japanese medicine nowadays. These three massage

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Approaches have all been licensed as forms of therapy by the Japanese government since 1955. Although they share some similarities, their underlying theories and practice and their common usage today are quite different:

Anma Is used to treat general discomfort and to release tension or stress. This therapy is most commonly practised amongst blind practitioners in Japan or amongst Shiatsu Practitioners in the West.

Shiatsu, Based on meridian theory, is used for both diagnosis and treatment of a wide range of disorders. It has become a very successful and popular therapy in many Western countries. Shiatsu Is also quite widely used for stress relief.

Western massage is most widely used in the treatment of muscular and skeletal problems, often in medical settings.

Anma

Anma Is the oldest of the massage traditions, having reportedly been brought over from China more than 1,500 years ago. It was once part of the mainstream of Japanese medicine but fell out of favour as Western massage approaches became more popular. Anma Then became almost exclusively the preserve of blind massage practitioners. (Massage has long been an accepted occupation amongst blind people in Japan.) These practitioners kept the therapy alive and it is now once again popular in Japan and taught to sighted practitioners as well.

Anma Is quite a vigorous form of massage designed more for therapy than for relaxation or pleasure. It involves gripping techniques where tense muscles are held and then released to ease muscle tension and promote blood circulation. Anma Also involves direct stimulation of acupoints along the meridian channels using mainly the fingers, thumbs, knuckles, and sometimes the elbows. Pressure is applied quite firmly and deeply, and the treatment is carried out fully clothed with no oil being used.

Anma Is ideal for treating tension-related ailments, muscular pain and stiffness, muscle strains, sports injuries, neck and shoulder problems, back problems, headaches, sinus problems, and so on.

Shiatsu

The term Shiatsu, Literally ‘finger pressure’, is a therapy that Tokujiro Namikoshi developed in the early 1900s, when he was just nine years old, using finger pressure massage to relieve his mother’s painful rheumatism.

Namikoshi’s Shiatsu Involves using the fingers, thumbs, and palms to apply pressure to the surfaces of the body in order to correct imbalances and promote health. Namikoshi believed that this type of therapy could stimulate the body’s natural healing mechanisms.

Various other forms of Shiatsu Have been developed by other Japanese masters over the years. One of the most well known is Zen-shiatsu, Developed by the great master practitioner, Shizuto Masunaga, which also employs the knees and elbows to apply firmer pressure and uses stretches to balance and realign the body.

Shiatsu Can be performed through clothing or directly onto the skin. As Shi-atsu Is a form of pressure therapy, oil isn’t used.

Western massage

Western massage was introduced to Japan by visiting European doctors in the early 1900s, and is based on Western anatomy and physiology. This massage involves vigorous kneading, grasping, and rubbing techniques designed to stimulate the sympathetic nervous system and release muscle tension. Most moves are directed from the extremities towards the heart in order to promote the return of circulating blood to the heart. Western massage is performed directly onto the skin and oil may be used.

Ampuku (abdominal massage and therapy)

Ampuku Therapy is diagnosis and therapy of the abdomen. As an ancient massage technique Ampuku Was banned during the American occupation of Japan after the Second World War but has enjoyed a revival, primarily amongst shiatsu practitioners in recent years.

Hara –

The HaraRefers to the lower part of the abdomen between the navel and the pelvic bone. The word Hara Literally means belly; in Japan this area is believed to be the centre of energy in the body. Its central point is the Tanden (known as the Dantien In Chinese), an acupoint located an inch and a half below the navel on the mid-line of the body. This point is known as ‘the sea of Ki As it is said that the Ki (vital energy) of the body generates there and then radiates throughout the body as a whole. This point is also held to be the centre of gravity in the body.

In the Japanese tradition, good health and well-being are believed to be connected to having a

Strong Hara. If your Hara Is strong, you stand tall; have a good posture; are calm, clear, and confident; and are able to ward off disease. A strong HaraIs also said to give you indomitable will-power that can be directed towards any activity that you undertake. In martial arts, the person with the strong Hara Is easily able to vanquish an opponent, even if they appear physically larger or stronger. The strong Hara Gives inner power that is believed to come from a renewable energy source that can be cultivated and utilised as necessary.

In Ampuku, The practitioner generally kneels beside you, as you lie on a mattress on the floor, and then gently probes the abdomen with the fingers to identify areas of Kyo (deficiency) and Jitsu (excess).

The hands are then used to balance these areas and to stimulate circulation within the abdominal area. This technique is believed to work on both a physical level (stimulating blood and lymph circulation) and also on an energetic level since the abdomen is the seat of the Hara - said to be the energetic powerhouse of the body.

Ampuku Treatment is believed to access and mobilise this powerhouse, enabling vital energy to circulate freely to areas of need in the body. It is on this basis that Ampuku Actually claims to be able to heal specific diseases rather than to simply offer massage for relaxation. In Japan, some practitioners still exist who practise solely Ampuku, Both diagnosing and treating through the abdomen alone.

In the West, Ampuku Is mainly incorporated as part of Shiatsu Therapy.

Japanese manipulation techniques

Various forms of home-developed manipulation therapies are practised in Japan, though osteopathy and chiropractic, popular in Europe, are rarely found. The most common manipulation therapies are the following:

IU Honetsugi: This therapy, literally meaning ‘bone-setting’, deals with sprains, strains, fractures, and dislocations and helps restore full movement and correct alignment to the joints.

IU Sei-tai: This therapy aims to facilitate structural realignment by bringing the body back to order. It involves gentle manipulations and soft-tissue work applied to the spine and joints, together with stimulation of acu-points with direct finger pressure. The idea is to correct postural imbalances, restore normal movement and alignment to the spine and joints, activate the body’s natural healing mechanism, and increase the vital energy supply to the internal organs. Nutritional and lifestyle advice may also be given.

IU So-tai: This bodywork system was developed by Dr Keizo Hashimoto, who found that his medical training didn’t enable him to heal patients with joint and pain problems effectively. He studied acupuncture and Sei-tai And then came up with the idea of ‘reverse motion treatment’ whereby the body is moved in the direction in which it feels most comfortable in order to release tension in the opposite side.

Dr Hashimoto also advocated that the treatment of joint pains should not be seen in isolation and should be combined with healthy breathing, eating, thinking, movement, and environment. There must be something in his approach for he lived to a healthy 96 years himself!

So-tai

Following the principle of ‘reverse motion treatment’ you first turn your head slowly to the left and right sides to see which moves more easily and which is stiff and/or painful. Then, instead of trying to increase the movement on the stiff/painful side, you first turn to the comfortable side. If this was your right side, you would turn your head fully to the right, stretching your neck muscles and looking over your right shoulder. At the same time you offer some resistance to this turn by placing your right hand against your right cheek and trying to push it back to the forwards position.

This resistance tricks the muscle into working harder and helps to release tension in the muscle in the opposite side. You then slowly release the hand and turn the neck back to the left side. Hey presto! – you should now find that you can turn farther to the left than before and with less discomfort.

This simple principle can be applied to other joints of the body and it really works! When I trained in So-tai, My teacher asked someone with severe neck restriction to come to the front for a demonstration. The woman had awakened with a stiff neck, was unable to turn to the left-hand side, and was in considerable discomfort. The teacher adopted the approach outlined above, standing behind the woman and placing one of her hands on the woman’s left shoulder and using the other to resist her turn to the right. She repeated this movement twice, each time asking the woman to return her head to the front. On the final release she asked the woman to turn her head to the left and there were gasps from the practitioner audience because she was suddenly able to look right over her left shoulder!

Japanese hydrotherapy

In Japan, bathing is a daily ritual and visiting mineral spa baths is a national pastime. The idea is that bathing can help ward off disease and different types of mineral waters at the various Onsen Spa baths around the country (of which more than a thousand exist) are highly prized for their particular healing properties. Spa baths may be hot or cold and the minerals they contain, such as sulphur and iron, are believed to help relieve arthritic, joint, and other health problems.

In the home, ingredients are sometimes added to baths for medicinal purposes. For example, you can add sliced ginger or mandarin orange peel to baths (usually dangled over the edge tied in a muslin pouch) to increase circulation and warm the body in winter and to prevent colds and flu. You can easily try out this practice for yourself!

Japanese dietary therapy

In Japan, it has long been believed that eating seasonal, fresh food in balanced combinations of colour and origin (that is, combining food from land, sea, and mountain in a single dish) is essential for health. Even ancient texts have detailed descriptions and diagrams of foods that are good to eat and which sorts of foods go well together or should not be combined.

One pioneering army doctor in the 1870s, Dr Sagen Ishizuka, spent many years identifying different types of food cures for various diseases and identified the importance of acid/alkaline balance in the body.

Dr Sagen Ishizuka’s ideas were further developed by one of his students, George Ohsawa, into a system known as macrobiotics (taken from the Greek Macro Meaning ‘big’ and Bio Meaning ‘life’) that has become popular in the West.

In this system, foods are classified according to the traditional Chinese medicine (TCM) principles of Yin (cooling foods such as lettuce and cucumber) and Yang (warming foods such as ginger). In a macrobiotic diet it is recommended that a balance of the two are consumed, with an emphasis on whole grains, vegetables, seaweeds, and so on, and that no dairy produce, refined sugar, chemicals, preservatives, or hot spices are consumed. An emphasis is also placed on alkaline-forming foods because it is believed that acidity contributes to many diseases such as arthritis and joint pain, acid regurgitation and digestive imbalance.

Spiritual medicine

In Japan, meditation, pilgrimages, ritual offerings and prayers are also seen as an aspect of personal healthcare. The idea of appeasing the gods still exists, even amongst people who are not particularly religious, and various gods within Buddhism are linked to health and healing. These include Yakushi, the medicine Buddha; Nikko-Bosatsu, god of sunshine and good health; and Fukurokuju, one of the seven gods of good fortune, who is the god of health and fitness. It is believed that praying and making offerings to these deities can help prevent or cure disease.

Several traditions of spiritual or energetic healing also exist in Japan involving such practices as the laying on of hands. The most well known in the West is Reiki healing. (Take a look at Chapter 20 for details on this therapy.)

Deciding When to Use Japanese Therapies

Many Japanese people use traditional therapies alongside orthodox Western medical treatment. Typically, the traditional therapies are preferred for chronic ailments such as arthritis, back pain, digestive imbalance, or general malaise, and Western medicine, as practised in state-of-the-art Japanese hospitals, is used for acute and serious conditions such as heart attack or ulcers. However, a cross-over also exists between the two.

When I lived and practised Asian medicine in Japan, I encountered many patients who used Western medicine for a diagnosis and treatment and then also visited an acupuncturist, Kanpo (herbal) specialist, or Shiatsu Or massage practitioner for either alternative or adjunct help. For example, people diagnosed with high cholesterol, gallstones, or non-insulin dependent diabetes would often have acupuncture or herbal treatment in an attempt to improve their condition and sometimes in order to avoid medication or surgery.

In the West, the most commonly used Japanese therapies are Shiatsu (mostly for relaxation but also for pain relief and relief from common ailments), acupuncture (for almost any kind of ailment but often for pain, menstrual problems, digestive problems, urinary problems, and headaches), and Kanpo (again for almost any condition but often for asthma and other respiratory complaints, skin problems, and more).

Exploring the Evidence for Japanese Medicine

In Japan, a considerable amount of research has been carried out on Kanpo Herbal medicine and acupuncture, although a lot of this work is in Japanese journals and not yet readily accessible to Western readers. Other Japanese medical approaches such as moxibustion, Shiatsu, And some of the other massage or manipulation therapies have little research evidence to support them.

Various trials in recent years have demonstrated the effectiveness of Kanpo Herbal medicine for conditions such as asthma, eczema, menstrual problems, and digestive disorders.

It appears that Japanese-style acupuncture may also help various conditions including pain relief, arthritis, migraines, headaches, and insomnia but it is hard to evaluate this research without being fluent in Japanese. Some research has also been carried out on Japanese acupuncture in France and America but it is quite limited and more is needed.

Finding a Practitioner of Japanese Medicine

To find a Japanese-style acupuncturist (who may also practise Japanese moxibustion, cupping, and other therapies), contact acupuncturists via the professional acupuncture associations (you can find these towards the end of Chapter 9) and ask if they practise Japanese-style acupuncture. Increasing numbers of Western trained acupuncturists are now training in this approach.

You can contact Kanpo Herbal medicine practitioners via the Register of Chinese Herbal Medicine (Www. rchm. co. uk) or the British Kanpo Association at the Kailash Centre, 7 New Court Street, London NW8 7AA (Tel: 020 7722 3939).

To find a Shiatsu Practitioner (who may also practise Japanese massage and manipulation therapies such as Anma, ampuku, And So-tai), Contact the Shiatsu Society (Tel: 0845 130 4560; Www. shiatsu. org), the Zen Shiatsu Society (Www. zen-shiatsu-society. co. uk), or Shiatsu International (Tel: 01787 880 005; Www. shiatsu-international. com). No professional regulatory requirements currently exist for practitioners of Shiatsu, But the General Shiatsu Council (GSC) is in the process of establishing a unified regulatory body for this therapy.

You can find international Sei-tai Practitioners at: Www. imoto-seitai. com/ english/ideology/index. html

For more information on macrobiotics and details of practitioners, contact the Macrobiotic Association of Great Britain (Www. macrobiotics. org. uk).

In This Chapter

Identifying the thoughts underpinning the way you feel Questioning your negative thoughts and generating alternatives ^ Using the ABC self-help forms to manage your emotions

F

■ n your endeavours to become your own CBT therapist, one of the key techniques you use is a tool known as an ABC form, Which provides you with a structure for identifying, questioning, and replacing unhelpful thoughts using pen and paper.

4

CBT therapists can sometimes use similar tools to the ABC form we offer in this chapter, all of which help patients to identify and replace negative thoughts. Different therapists may refer to these forms as Thought records, thought diaries, daily records of dysfunctional thoughts, Or Dysfunctional thought records (DTRs). Fret not – in general, all of these forms are simply different ways of saying largely the same thing: Your thinking impacts on your feelings and actions.

The way you think affects the way you feel. Therefore, changing your unhelpful thoughts is a key to feeling better.

In this chapter, we give you two versions of the ABC form: one to get you started with identifying your triggers, thoughts, and feelings, and another that takes you right through to developing alternative thoughts so you can act differently in the future.

Catching NATs

Getting the hang of the ABC form is often easier if you break down the process into two steps. The first step is to fill out the first three columns (Activating Event, Beliefs And thoughts, Consequences) Of the form, which you can find further on in this chapter (ABC Form I). This gives you a chance to focus on catching your Negative automatic thoughts (NATs) on paper and to see the connection between your thoughts and emotions.

Using the ABC form is great, but if you don’t have one to hand when you feel an upsetting emotion, grab anything you can write on to scribble down your thoughts and feelings. You can always transfer your thoughts to a form later.

Making the thought-feeling link

A crucial step in CBT is to make the Thought-feeling link Or B-to-C connection; That is, seeing clearly for yourself the connection between what goes through your mind and your resulting emotions. When you see this connection, it can help you to make much more sense of why to challenge and change your thoughts.

Becoming move objective about your thoughts

One of the biggest advantages of writing down your thoughts is that the process can help you to regard these thoughts simply as hunches, theories, and ideas – rather than as absolute facts.

IkBEfl The more negative the meaning you give to an event, the more negative you’ll

Feel, and the more likely you’ll act in a way that maintains that feeling, Lilil ) Crucially, when you feel negative, you’re more likely to generate negative thoughts. See how easily you can get caught in a vicious circle? Just one of the reasons to take your negative thoughts with a bucket of salt!

Stepping Through the ABC Form 1

So, time to embark on this major CBT self-help technique using Figure 3-1. The basic process for completing the ABC form is as follows:

1. In the ‘Consequences’ box, point 1, Write down the emotion you’re feeling.

Therapy’s about becoming emotionally healthier and acting in a more self-helping or productive way. So, when you’re filling out the ABC form, the most logical place to start is with the emotion you’re feeling.

Emotions and behaviour are Consequences (C) of the interaction between the Activating event or trigger (A) and the Beliefs or meanings (B) in the ABC model of emotion.

Examples of emotions you may choose to list in the ‘Consequences’ box include:

• Anger

• Anxiety

• Depression

• Envy

• Guilt

• Hurt

• Jealousy

• Shame

Fill out an ABC form when you feel emotionally upset, when you’ve acted in a way that you want to change, or when you feel like acting in a way that you wish to change. We give you more information on how to help you understand and identify emotions in Chapter 6.

2. In the ‘Consequences’ box, point 2, write down how you acted.

Write down how your behaviour changed when you felt your uncomfortable emotion. Examples of the behaviour that people often identify in this box include:

• Avoiding something

• Becoming withdrawn, isolated, or inactive

• Being aggressive

• Binge-eating or restricting food intake

• Escaping from a situation

• Putting off something (procrastination)

• Seeking reassurance

• Taking alcohol or drugs

• Using safety behaviours, such as holding on to something if you feel faint

3. In the’Activating Event’ box, write down what triggered your feelings.

As we discuss in Chapter 1, the A in ABC stands for Activating event or trigger, Which are the things that triggered your unhelpful thoughts and feelings. Activating events or triggers to put in this box can include:

• Something happening right now

• Something that occurred in the past

• Something that you’re anticipating will happen in the future

• Something in the external world (an object, place, or person)

• Something in your mind (an image or memory)

• A physical sensation (increased heart rate, headache, feeling tired)

• Your own emotions or behaviour

An activating event can be pretty much anything. Use your feelings – rather than whether you think the event is important – as a guide to when you should fill out a form.

To keep your ABC form brief and accurate, focus on the specific aspect of the activating event that you’re upset about. Use the table of emotions in Chapter 6 to help you detect the themes to look out for if you’re unsure about what may have triggered your thoughts and feelings.

4. In the ‘Beliefs’ box, write down your thoughts, attitudes, and beliefs.

Describe what the event (whatever you’ve put in the ‘Activating Event’ box) meant to you when you felt the emotion (what you’ve written under point 1 in the ‘Consequences’ box).

The thoughts, attitudes, and beliefs you put in ‘Beliefs’ box often pop up reflexly. They may be extreme, distorted, and unhelpful – but they may Seem Like facts to you. Some examples of these NATs include:

• Here I go again, proving that I’m useless!

• I should’ve known better!

• Now everyone knows what an idiot I am!

• This proves that I can’t cope like normal people do!

Thoughts are what count, so think of yourself as a detective and set out to capture suspect thoughts. If your thoughts are in the form of a picture, describe the image, or what the image means to you – write them down in the ‘Beliefs’ box.

We think not only in words but also in pictures. People who are feeling anxious frequently describe that they see Catastrophic images Going through their mind. For example, if you fear fainting in a restaurant, you may get an image of yourself on the restaurant floor with staff fussing over you.

5. In the ‘Thinking Error’ box, consider what your thinking errors may be.

One of the key ways to become more objective about your thoughts is to identify the Thinking errors That may exist in the thoughts you list in this box. (Have a look at Chapter 2 for more details on common thinking errors.)

= CO "

— or*

Date

Activating Event

3. Write down what triggered yourfeelings:

Consequences

1. Write down your emotion:

2. Write down your actions:

The ABC Form #1

Beliefs

4. Write down the thoughts and beliefs that went through your mind:

Thinking Error

5. Identify the thinking errorfor each thought:

Questions that you might ask yourself in order to identify your thinking errors include:

• Am I jumping to the worst possible conclusion? (Catastrophising)

• Am I thinking in extreme – all-or-nothing – terms? (Black-and-white thinking)

• Am I using words like ‘always’ and ‘never’ to draw generalised conclusions from a specific event? (Overgeneralising)

• Am I predicting the future instead of waiting to see what happens? (Fortune-telling)

• Am I jumping to conclusions about what other people are thinking of me? (Mind-reading)

• Am I focusing on the negative and overlooking the positive? (Mental filtering)

• Am I discounting positive information or twisting a positive into a negative? (Disqualifying the positive)

• Am I globally putting myself down as a failure, worthless, or useless? (Labelling)

• Am I listening too much to my negative gut feelings instead of looking at the objective facts? (Emotional reasoning)

• Am I taking an event or someone’s behaviour too personally or blaming myself and overlooking other factors? (Personalising)

• Am I using words like ‘should’, ‘must’, ‘ought’, and ‘have to’ in order to make rigid rules about myself, the world, or other people? (Demanding)

• Am I telling myself that something is too difficult or unbearable or that ‘I can’t stand it’ when actually it’s hard to bear but it Is Bearable and worth tolerating? (Low frustration tolerance)

Creating Constructive Alternatives: Completing the ABC Form 11

When you feel more confident about identifying your As, Bs, Cs, and thinking errors, you can move on to the ABC form II. This second form helps you question your unhelpful thoughts in order to reduce their intensity, generate and rate the effects of alternative thoughts, and focus on acting differently.

The first five steps for completing the ABC form II (see Figure 3-2) are the same as those for the ABC form I. Then come five more steps. You can find a blank version of the ABC form II in Appendix B. In the ABC form II, column A is the Activating Event, column B is Beliefs, column C is for Consequences, column D is Dispute, and column E is Effect.

6. Examine your negative thoughts more closely.

Ask yourself the following questions in order to examine and weaken your unhelpful thoughts:

• Can I prove that my thought is 100 per cent true?

• What are the effects of thinking this way?

• Is my thought wholly logical or sensible?

• Would people whose opinions I respect agree that this thought’s realistic?

• What evidence exists against this thought?

• Is my thought balanced, or extreme?

• Is my thought rigid or flexible?

• Am I thinking objectively and realistically, or are my thoughts being biased by how I feel?

Consider long and hard your negative or unhelpful thoughts in the light of the preceding questions. Don’t simply give glib ‘yes’ or ‘no’ answers. Instead, think things through and perhaps write down your challenges to your unhelpful thoughts in column D. See the list of questions and prompters at the bottom of the ABC form II, which can help you further with this.

7. Generate alternatives for each of your unhelpful thoughts, attitudes, and beliefs.

This step is critical as it’s your alternative thoughts that will help you to feel better! In column D, write down a flexible, non-extreme, realistic, and helpful alternative for each thought, attitude, or belief that appears in column B. The following questions may help you to generate some alternatives:

• What’s a more helpful way of looking at the situation?

• Do I encourage friends to think in this way?

• When I’m feeling OK, how do I think differently?

• Have any past experiences shown me that another possible outcome exists?

• What’s a more flexible or less extreme way of thinking?

• What’s a more realistic or balanced way of thinking that takes into account the evidence that does Not Support my thought?

• What do I need to think in order to feel and act differently?

Some thoughts are more stubborn than others, and you won’t turn your thinking around completely in one go. Wrestling with NATs for a while before they weaken is typical and appropriate. Think of yourself as Training Your mind to think more flexibly and constructively over a period of time.

Some intrusive thoughts, images, and doubts can be made worse if you engage with them. If you have obsessive-compulsive disorder (OCD), health anxiety, body dysmorphic disorder (BDD), worry, or a jealousy problem, be sure to develop the capability to live with doubt, and allow catastrophic thoughts to pass through your mind rather than challenging them. We explain this in more depth in Chapter 5, Chapter 9, and Chapter 11. So if you think you need to learn to live with doubt, or to tolerate upsetting, intrusive thoughts in general, we suggest steering clear of using ABC forms for these problems.

8. In column E, rate the effects of your alternatives on your feelings.

Rate your original feelings 0-100 per cent. Also note whether you experience any alternative healthier emotions such as:

• Concern

• Annoyance

• Sadness

• Remorse

• Disappointment

• Sorrow

You won’t always notice a great deal of change in how you feel at first, so keep persevering!

9. Develop a plan to move forward.

The final step on the ABC form II is to develop a plan to move forward. Your plan may be to conduct a behavioural experiment to help you gather more information about whether your thoughts are true or realistic, or to behave differently in a specific situation. Refer to Chapter 3 and Chapter 4 for more ideas.

J^S-g I

Mil

Date March 18th The’ABC Form #11

Disputing {Questioning and Examining) and Generating Alternative Thoughts, Attitudes, and Beliefs:]. Identify your ‘thinking errors’ at B (e. g. Mind Reading, Catastrophising, Labelling, Demands etc.). Write them next to the appropriate ‘B’. 2. Examine whether the evidence at hand supports that your thought at B Is 100% true. Consider whether someone whose opinions you respect would totally agree with your conclusions. 3. Evaluate the helpfulness of each B. Write down what you think might be a more helpful, balanced and flexible way of looking at A. Consider what you would advise a friend to think, what a role model of yours might think, or howyou might look at A If you were feeling OK. 4. Add evidence and arguments that support your alternative thoughts, attitudes and beliefs. Write as if you were trying to persuade someone you cared about.

An ABC a day keeps the doctor at bay!

Ifyouwantto master any skill, rememberthese three words: Practice, practice, practice/You May not need to fill out an ABC form everyday. Other days, you may need to complete more than one form. The point is, that practising ABC forms regularly is worthwhile because:

Practice helps change disturbing feelings and the thoughts that underpin them.

Sinking a new thought into your head and heart takes repetition.

By completing forms on paper, you can become increasingly able to challenge unhelpful thoughts in your head – although you may still need to do it on paper sometimes.

As you progress inyour abilityto overcome difficulties and develop your CBT self-help skills, you may still find the ABC form useful when you’re hit with a biggy. And remember: If you can’t work out your unhelpful thinking on the hoof, do sit down and bash it out on paper.

10. Set yourself some homework.

When you’ve completed several ABC forms, you may well begin to notice recurring themes, thoughts, attitudes, or beliefs. Such repetitions may suggest that you need to add some other CBT techniques in order to overcome certain emotions or behaviours, for example:

• Facing a fear until it reduces (Chapter 9)

• Conducting a behavioural experiment to test out a thought (Chapter 4)

• Acting repeatedly ‘as if you believe an alternative thought, attitude, or belief (Chapter 15)

• Completing a Zig-Zag form to strengthen an alternative thought, attitude, or belief (Chapter 15)

Read on and set yourself some more therapy assignments using the CBT principles in this book.

Keeping your old ABC forms can be a rewarding record of your progress, and a useful reminder of how to fill them in if you need to use one again in the future. Many of our clients look back over their ABC forms after they feel better and tell us: ‘I can’t believe I used to feel and think like that!’

Chapter 4

In This Chapter

^ Covering the mathematics of probability computations ^ Computing the probabilities of desired outcomes ^ Figuring the odds

The concept of probability is all around us. You can’t turn on the TV or radio or pick up a newspaper or magazine without hearing or reading about the probability of some event. From predicting the probability of a hurricane hitting land to declaring the odds that a horse will win the Kentucky Derby, predictions are rampant. The predictions themselves may not be correct, but probability isn’t a For sure, It’s just a Probably.

This chapter starts out by showing you how to do the computations needed for solving probability problems. (If you need a more thorough review of the relationships between fractions, decimals, and percents, and how to change from one to another, refer to Chapter 5.) In this chapter, you use the percentages to make the predictions. And you see what the odds are that you’ll just Love This topic.

Defining and Computing Probability

The Probability Of an event is the likelihood that it’ll happen. The most common way to express a probability is with a percent, such as 60 percent probability of rain or 70 percent likelihood that he’ll hit the ball. Probability is also expressed in terms of fractions — in fact, a fraction supplies one of the nicest ways of defining how you get the probability of something happening.

When the probability of something happening is 95 percent, you can be pretty sure that the event will happen — 95 out of 100 times it does. A probability of 15 percent is pretty low. That sounds like the chance that I’ll make a free throw in basketball.

Counting up parts of things for probability

Following is a standard version of a probability formula. This formula allows for you to count up how many different ways something can be done and then determine the probability that just a few of those things will happen.

The probability, P, That an event, E, Will happen is found with:

P ,eh = Number of ways event E Can happen ^ h total number of ways all events can happen

For example, consider a jar of marbles and the probability that you’ll pick a red one. Or you look at the seats in an airplane and determine the probability of your getting a particular seat. Or how about the number of boys in a family? How does a number of boys become a probability problem? (Well, boys can be a Problem — I don’t know about the probability part.)

Dealing with a jar that contains 10 red, 20 yellow, and 50 green marbles

Picture a jar containing marbles and a task of drawing a marble out of the jar. You have your eyes blindfolded, and you can’t tell the difference between the marbles by feeling them — they’re all the same size.

The Problem: What is the probability that you get a green marble when you choose a marble at random out of the jar that contains 10 red, 20 yellow, and 50 green marbles?

Make a fraction that has the number of green marbles in the numerator and the total number of marbles in the denominator. Then reduce the fraction and write your final answer as a percent. (Go to Chapter 5 if you need help changing a fraction to a percent.)

Number of green marbles

P _ Green I = . . ,-7s-1-n—

Total number of marbles

= |0 = 5 = 0.625 = 62.5 percent

A probability of 62.5 percent isn’t particularly high, but it’s better than half. If you had to guess which color marble you might draw at random, you’d pick the green marble, because it has the highest probability (more greens than any other color).

The Problem: What is the probability that you’ll choose a marble at random and that it’s Not Green if the jar contains 10 red, 20 yellow, and 50 green marbles?

You have two ways of doing this. The first is to find the number of marbles that are Not Green and divide by the total number of marbles.

P (not green):

Number of red or yellow marbles

Total number of marbles

30 80

0.375 = 37.5 percent

Even adding the red and yellow marbles together, you still have a better chance of drawing a green marble. The other way of solving a probability problem that has a Not In it is to subtract from 100 percent.

The probability than an event, e, will Not Occur is 100 percent minus the probability that it Will Occur. P(not e) = 100 percent – P(e).

So, to solve for the probability that the marble is Not Green, you take the probability that it Is Green and subtract that from 100 percent. Subtracting, you get 100 percent – 62.5 percent = 37.5 percent.

The Problem: You have a jar that contains 10 red, 20 yellow, and 50 green marbles, and you take a marble out of the jar and put it in your right pocket without looking at the color. Now you draw another marble out of the same jar and put it in your left pocket. What is the probability that both marbles are red?

Right away, you should be thinking about how unlikely the probability is that both marbles are red. The red marbles are the fewest in the jar. The probability should be pretty low. To do the problem, first find the probability of drawing a red marble out of the 80 marbles, and then find the probability of drawing another red marble out of the 79 remaining marbles.

The probability that an event, E, And another event, f will Both Occur is equal to the product of the two probabilities. P(e and f) = P(e) x P(f).

The probability of drawing a red marble is P (red) = ^ = ‘g’ = .125 = 12.5

Percent. If that first marble is red, then there are only 9 red marbles left in the jar of 79 marbles. So the probability of a second marble being red is

P (red) = 79 . .114 = 11.4 percent. Multiply the two probabilities together.

12.5 percent x 11.4 percent = 0.125 x 0.114 = 0.01425 or about a 1.4 percent chance that both marbles are red.

Looking at 40 rows of seats on an airplane, with 7 seats per row

Nowadays, you can make your plane reservations online and, in some cases, even pick your seats. The following problems involve the case where you’re on standby and don’t get a seat assignment choice — you’ll be happy just to

Get on the airplane. So assume that the seat assignment is selected at random. Imagine that all 40 rows in the airplane have 7 seats across: 2 seats on either side along the windows, and 3 seats in the middle. So there are 40 x 7 = 280 seats possible.

The Problem: What is the probability that your seat will be in row 10 if there are 40 rows with 7 seats in a row?

Take the number of seats in row 10, which is 7, and divide by the total

71

Number of seats, 280. P (row 10)

280 40

0.025 =2.5 percent. The

Probability is only 2.5 percent. Sorry — you’ll be disappointed if 10 is your lucky number and you were hoping for that row.

The Problem: What is the probability that you’ll get a window seat if there are 40 rows with 7 seats in a row?

Determine the number of window seats. With 40 rows and a window seat at each end of each row, that gives you 40 x 2 = 80 window seats. Divide 80 by the

Total number of seats. P (Window) = = 28 = 7 555 0.2857 = 28.57 percent.

Notice that you’d get the same answer if you just did the computation on a

Single row. Two of the seven seats are window seats. The fraction 2 applies

7

To figuring the probability of a window seat either in one row or the whole plane.

The Problem: What is the probability that you’ll get a seat either in the last 4 rows or a window seat, if there are 40 rows and 7 seats in a row?

When counting the number of seats for this problem, you have to be careful not to count the same seats more than once. Some of the seats in the last four rows are also window seats.

When counting a number of items in two sets or categories, you first add up the number of items in one category plus the number of items in the second category, and then you subtract the number of items that they share. Let N Represent "the number in":

N(Set 1 or Set 2) = n(Set 1) + n(Set 2) – n(Set 1 and Set 2)

Applying this rule to the seats on the plane, there are 4 x 7 = 28 seats in the last four rows and 2 x 40 = 80 window seats. The last four rows have 4 x 2 = 8 window seats. So the number of seats you want is: 28 + 80 – 8 = 100 seats that are either in the last four rows or a window seat (or both). The probability that you’ll get one of those seats is found with

P (Last 4 or window) = -280 = 28 = 14 555 0.3571 = 35.71 percent.

Seeing whether a family of three children has a certain number of boys

Some classic probability problems have to do with children in a family and determining the likelihood that all three are boys or, maybe, that there are two boys and a girl, and so on. A wonderful way to handle problems like this (when it’s possible) is listing all the possibilities and counting the number of possibilities you want. In a family of three children, the eight possible arrangements of boys (B) and girls (G), listing the children in order, are: BBB, BBG, BGB, GBB, BGG, GBG, GGB, and GGG. Notice that two of the arrangements are all one sex, three of the arrangements have two boys and one girl, and three of the arrangements have one boy and two girls. None of the arrangements is the same.

The Problem: When choosing a three-child family at random, what is the probability that the children are all the same sex?

Count the number of arrangements with all the same sex and divide by the total number of arrangements. Three children in a family can be arranged in the following eight ways: BBB, BBG, BGB, GBB, BGG, GBG, GGB, and GGG.

21

P (3 same) = 8 = 4 = 0.25 = 25 percent. In 25 percent of three-child families, the children are all the same sex.

The Problem: What is the probability that a three-child family has at least one girl?

V£?LA/v You can count how many of the arrangements of BBB, BBG, BGB, GBB, BGG, GBG, GGB, and GGG have one or more girls and find that there are seven of

7

Them. P (at least one girl) = 8 = 0.875 = 87.5 percent. Another approach,

Instead of counting how many families have a certain characteristic, is to use the Not Idea and subtract from 100 percent. (Refer to the "Dealing with a jar that contains 10 red, 20 yellow, and 50 green marbles" section, earlier in this chapter, for the rule.) Applying the Not Rule to this problem, determine how many arrangements have No Girls — there’s only 1. Find the percentage,

P (no girl) = 8 = 0.125 = 12.5 percent. Then subtract 100 percent -

12.5 percent = 87.5 percent.

Using probability to determine sums and numbers

When you have a percent or fraction that represents a probability, you can use the decimal equivalent of the percent or the fraction to determine a

Sons and daughters

In the Jefferson family, each daughter has the has brothers. How many sons and daughters same number of brothers as she has sisters, are there in this family? and each son has twice as many sisters as he

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Number of times that something may happen. The number answer may represent how many coins in a pouch are gold or how many moves you may be making while playing a board game. The probability value always assumes that you’re using fair dice (each face equally likely to appear) or a fair coin (not weighted on one side or the other) or aren’t peeking or aren’t in some way altering the numerical value.

Rolling a die with faces of 1, 2, 3, 4, 5, and 6

When you roll a die, one of the faces lies on the table, and the other five faces are showing. The face that counts, in most games, is the face on the top of the die, after it’s been rolled.

The Problem: You’re nearing the end of a game of Trivial Pursuit and are just three spaces away from trying for the last pie piece (for non-Pursuit people, it’s the last of six categories). You shake and shake and shake your die before rolling it. What is the probability that you’ll roll either a 3 or a 5 (a 5 will allow you to roll again)?

AVLAjV Make a listing of all the possible results of the roll and a listing of all the num-F Bers that you want to get. With six faces on the die, there are six different

W\f J possibilities: 1, 2, 3, 4, 5, or 6. You want one of two different rolls: 3 or 5

(although you’d prefer the number 3), so you divide 2 by 6 to get about

0.3333 or 33.33 percent.

Rolling a die and flipping a coin at the same time

When you roll a standard die, you get 1, 2, 3, 4, 5, or 6. When you flip a coin, you get either heads or tails. Do the two actions at the same time (which takes some coordination not to have at least one fall on the floor) and you have the following results possible (let H represent Heads And T represent Tails): 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, or 6T.

The Problem: When you roll a die and flip a coin at the same time, what is the probability that you get an even number on the die with tails?

Count up how many of the results have an even number (2, 4, or 6) and tails,

At the same time. The results you want are: 2T, 4T, or 6T. That’s 3 out of the

31

12 possible results. P (Even and tails) = j2 = 4 = 0.25 = 25 percent.

The Problem: When you roll a die and flip a coin at the same time, what is the probability that you get Either An even number Or Tails?

^VLA/V Note that this problem is different from the previous problem where you wanted Both An even number and tails at the same time. In this case, you’ll take either an even number or tails, or both. You can’t just add up the number of even numbers and the number of tails. That sum is 6 + 6 = 12, which is the same number as all the choices. You can look through the list and find all the choices that have either an even number or tails (or both) and get: 2H, 4H, 6H, 1T, 2T, 3T, 4T, 5T, or 6T, which is 9 items. The other method to use is the counting rule (refer to "Looking at 40 rows of seats on an airplane" for more on the counting rule) and get n(even or tails) = n(even)

+ N(tails) – N(both even and tails) = 6 + 6 – 3 = 9. In any case, the probability

93

Is computed P (Even or tails) = y2 = 4 = 0.75 = 75 percent.

Rolling two dice at the same time

Board games like Monopoly involve moves based on the results of rolling two dice at the same time and adding up the face values. The sums that you get from adding the two numbers on the dice are any of the 11 numbers from 2 through 12, but there are 36 different ways to get those 11 numbers. The sums are best shown with a table of values. In Table 8-1, the face values of the two dice are shown along the top and down the left side. The sums are shown in the table.

2 2 + 1 = 3 2 + 2 = 4 2 + 3 = 5 2 + 4 = 6 2 + 5 = 7 2 + 6 = 8

You probably notice, in the table, that the numbers increase as you move down a column or across a row. Did you also notice that the sums in the diagonals are the same? The longest diagonal is the one with the sums of 7 — it has six entries that add up to 7.

The Problem: What is the probability that, when you roll two dice, you’ll get a sum of 6?

V£?LAjV Referring to the table, you see that there are five different ways to get a sum

Of 6; the sums are all found on a diagonal starting under the 5s column and

Moving downward to the left. Make a fraction putting 5 in the numerator and

5

36 in the denominator. P (Sum of 6) = gg ~ 0.1389 = 13.89 percent.

The Problem: You’re playing Monopoly and sitting on the railroad right before reaching Go. You’re also looking at Park Place and Boardwalk with your opponent’s hotels, waiting for you to land on them. What is the probability that you’ll roll a sum large enough to miss those hotels completely (you need a sum of 5 or more)?

^VUUV You can refer to Table 8-1 and count up all the sums that are 5 or greater.

Then put the number of sums you count over 36 and divide. An even easier task would be to count up those sums that are Less than 5, find the probability, and then subtract that probability from 100 percent. (Refer to the "Counting up parts of things for probability" section for more on how the rule for Not Works.) You see six different entries in the table that are sums of 4 or less.

P (sum 4 or less) = 36 = – g. 0.1667 = 16.67 percent. Subtracting

100 percent – 16.67 percent = 83.33 percent.

The Problem: When you roll two dice, what is the probability that the sum will be even or that the roll will be a Doubles (both faces the same)?

V£.VLA/l/ Count up the number of rolls that have an even sum, and then go along the diagonal to count up all the doubles. Subtract the rolls that the two categories have in common. N(even sums) + N(doubles) – N(even sums that are doubles) = 18 + 6 – 6 = 18. All of the doubles are even sums, of course. Twice a number (any Number) is an even number. So the probability is found by dividing 18 36, which is half, and the probability is 50 percent.

Making words from words — or not

If you’re like me, you’ve have had at least one teacher who sought to entertain you and your classmates on the day before a school holiday by having you make words from the letters in the name of the holiday, whatever the holiday was. Being a word junky, myself, I always liked these exercises. Those who aren’t that much into words will just have to indulge me a bit.

The rules for making words in statistical or probability problems is that the arrangement of letters doesn’t have to actually form a real word. A better term than Word In this process is Arrangement. You just list all the different Arrangements Of letters possible. For example, you can make a list of 12 different 2-letter words (arrangements) formed from the letters in MATH. These words are: MA, MT, MH, AM, TM, HM, AT, AH, TA, HA, TH, HT. Of those 12 arrangements, the only words that are actually found in the dictionary are: MA, AM, AT, AH, and HA. (No, you can’t use TA; it’s an abbreviation for one of the elements in the periodic table, for teaching assistant, and for numerous other things as well.)

The Problem: You have the four Scrabble tiles M, A, T, and H in a bag. Drawing out two of the letters, what is the probability that you can form an English word with the two letters?

Of the 12 different arrangements possible with the four letters in the

Word MATH, five of them form words, so the probability computed is 5

P (A word) = J2 . 0.4167 = 41.67 percent.

The Problem: You have the six Scrabble tiles S, T, A, R, E, and D in a bag. Drawing out two of the letters, what is the probability that you’ll draw one vowel and one consonant?

^.VLA/V This time, you don’t need to worry about the order of the letters, just the

Type of letter that they are. List all the different possibilities, but don’t list the same two letters in different orders (don’t list both S and T and T and S). The 15 different possibilities are: ST, SA, SR, SE, SD, TA, TR, TE, TD, AR, AE, AD, RE, RD, ED. Of the 15 possibilities, 8 have 1 vowel and 1 consonant. Doing the

Math, P (one vowel, one consonant) = . 53.33 percent.

Predicting the Outcomes

Some probabilities are Empirical (determined by observations or experiments) and other probabilities are Theoretical (determined using mathematical formulas). For instance, the probability that a person will have type-O blood is empirical — determined over the years from testing the blood of millions of people. The probability that a person will win the lottery is theoretical — it can be computed using mathematical formulas. But these are just probabilities. Neither guarantees or forbids anything. Each determines a likelihood of something occurring. No matter how likely something will happen, there’s still the chance that it won’t happen.

Predicting using empirical probabilities

The weather is one of the most frequently talked-about probability situations. You get predictions on temperature, precipitation, humidity, and long-term trends.

Seeing that the probability of rain is 70 percent

You hear on the radio that for the month of April, the probability of rain will be 70 percent. This means that, 70 percent of the time, it’ll be raining on a day in April. This is just a prediction, of course, but it’s computed using past trends and observations of what’s going on around the world.

The Problem: You’re planning on an April wedding. If the prediction is that there’s a 70 percent chance of rain on any day in April, how many days does that leave you to try to plan a dry-weather wedding?

Vj. VLAAf You’re going to assume that the dry periods will occur on full days — just to make the math simpler. (And you certainly don’t want it to rain for 70 percent of the time Every Day!) If it’s going to rain on 70 percent of the days, then it should be dry for 30 percent of them. Multiply the number of days in April, 30, by 30 percent to get 30 X 0.30 = 9. You have nine days to choose from for your wedding. Lots of luck!

Using the probability of being struck by lightning

The probability of being struck by lightning is a pretty low number, even if that probability is applied to every year of your life. Of course, your lifestyle can change that probability somewhat — depending on how much you go golfing or sailing.

The Problem: If the population of the United States is 300 million, and the probability of a person being hit by lightning is 0.00003 percent, then how many people do you expect to be hit by lightning this year?

You will multiply the number of people by the probability of being hit by lightning. Watch out for the two numerical challenges. The 300 million has to have zeros added, and the percentage has to have its decimal place changed before multiplying. The computation: 300,000,000 X 0.0000003 = 90 people in the United States who are expected to be hit by lightning.

Working with a probability of having type-O blood

If you have type-O blood, then you’re very popular with the local hospitals and blood banks, because you’re a universal donor. Approximately 45 percent of the population has type-O blood, 40 percent has type-A blood, 11 percent has type-B blood, and 4 percent has type-AB blood. Along with the four blood types in terms of letters, you are either RH+ or RH-. So, technically, there are eight different blood types: O+, O-, A+, A-, B+, B-, AB+, and AB-.

The Problem: You have type B+ blood and need a blood transfusion. You can use either type-O or type-B blood and can use either a + or – RH factor. What is the probability that a person selected at random can be a donor for you?

Determine the total percentage of eligible donors by adding the probabilities together: 45 percent + 11 percent = 56 percent.

The Problem: You work for the Red Cross blood services and need to secure some O- blood to have on hand for the imminent birth of quadruplets at the local hospital. Of the 45 percent of the population that has type-O blood, about 16 percent of the type-O people are O-. About how many people out of 100 has O- blood (what is the probability that a person selected at random out of 100 has O – blood)?

^VLA* Percentages are out of 100. So, if 45 percent of the population has type-O blood, then chances are that 45 out of 100 have type-O blood. If 16 percent of the type O people have O – blood, then find 16 percent of 45 with 0.16 X 45 = 7.2. About 7 people in 100 have O – blood. The probability of a person at random having O- blood is about 7.2 percent.

Counting on Jimmy batting 300

When you say that a baseball player is Batting .300, This means that his percentage is 300 out 1,000 or 30 percent. So the probability that he’ll get a hit when he goes to bat is 30 percent.

The Problem: Jimmy is first in the lineup and typically gets to bat four times each game. His team is playing Chicago this weekend and they’ll play four games in all. Jimmy is batting.300. How many hits do his fans expect him to get?

In the four-game series, Jimmy expects to bat 4 X 4 = 16 times. The probability of a hit at any time at bat is 30 percent, so multiply 16 X 0.30 = 4.8. Jimmy is expected to get about five hits.

Using theoretical probabilities

Theoretical probabilities are determined using mathematical counting techniques and mathematical formulas. These probabilities are still just that: predictions or likelihoods of events happening.

Betting on heads or tails

When flipping a fair coin, the probability is 50 percent that it’ll be heads and 50 percent that it’ll be tails.

The Problem: What is the probability of flipping three heads in a row?

This problem can be done one of two ways: Multiply the probability three times or make a list of possibilities and write a fraction. The probability of getting heads is 50 percent. The probability of heads the first time And The second time is 50 percent X 50 percent. Carry that one more step for three flips, and you get 50 percent X 50 percent X 50 percent = 0.50 X 0.50 X 0.50 = 0.125 = 12.5 percent. The chance of three heads in a row isn’t very good. The other method, making a list instead of multiplying, has you write down all the possibilities of flipping three coins: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. You see 8 different arrangements, and

1 out of 8 is P (Three heads) = 8 = 0.125 = 12.5 percent.

Working with the probability of winning the lottery

You have a better chance of being struck by lightning than of winning the lottery! Earlier in this chapter, I tell you that the probability of a person being hit by lightning is 0.00003 percent. And, as low as that probability is, it’s better than your chance of winning the lottery. The probability of winning the lottery is mathematically generated; the lightning probability comes from observations (and not all strikes are reported).

A certain state has a lottery in which you have to guess which 6 of 54 numbers will be drawn on Saturday night. Your favorite numbers are: 10, 16, 17, 19, 26, and 28.

The Problem: The probability of winning a lottery, where you have to pick six numbers from the numbers 1 through 54, is 0.00000387 percent. How many tickets do you have to buy (and combinations of numbers do you have to choose) to be sure that you have a ticket with all the winning numbers on it?

The percentage is the probability that one ticket will be the winning ticket. Divide the number 1 by the percentage to get the number of tickets needed (the probability is 1 out of that number of tickets). 1 0.0000000387 ~ 25,830,000 tickets. This is a rounded number, because the probability was rounded and most scientific calculators won’t give the exact value. In any case, there isn’t enough time in a week to buy all the tickets, even if you had the money to do it.

Dealing with the probability of drawing an ace

A standard deck of playing cards has four different suits (spades, hearts, diamonds, clubs) and 13 different cards in each suit. Whether you’re playing poker or bridge or hearts or euchre, the probability of a particular card or a particular suit plays a big part in the result of the game. The rest of the game depends on your skill and your partner.

The birthday problem

Even though there are 366 different birthdays possible, you only need to have about 24 people in a room to have a better than 50 percent chance that two people will have the same birthday (not the year, necessarily, just the

Date). In a room of 40 people, the probability is almost 90 percent that two people will have the same birthday. Next time you’re in a boring meeting, try it by surveying the gathering.

The Problem: You’re playing hearts with three other players. You’re trying to decide what card to play. What are the chances that the person to your left has the queen of spades?

VLAiV First, assume that you do Not Have the queen of spades. (Otherwise, why

Would you need to find the probability?) The cards remaining to be played are divided among four players. It doesn’t matter how many cards have yet to be played — and you’re only worried about three-fourths of them, because you know what cards you have. One out of the other three players has the queen of spades. Back to the question: what is the probability that the person to your left has the queen of spades? After wading through all the extra information, you determine that the probability is 1 ■ 3 = 0.3333 or about 33.33 percent chance that it’s the person to your left with the queen of spades.

The Problem: You’re drawing a card from a standard deck of playing cards. What is the probability that you’ll draw either an ace or a club?

■A? LA* Use the counting method from the "Counting up parts of things for probability" section to get the number of cards in the category that you want: an ace or a club. N(aces) + N(clubs) – N(ace of clubs) = 4 + 13 – 1 = 16 cards. A full deck has

52 cards, so divide 16 52. P (an ace or a club) = ^ = 13 ~ 0.3077 = 30.77 percent.

Figuring Out the Odds

The probability that something will happen and the odds of it happening are closely tied by the mathematics involved. If the probability of an event is 50 percent, then the odds of the event are 1 to 1 (one that it will, and one that it won’t).

Changing from probability to odds and back again

The probability of an event is a percentage between 0 percent and 100 percent, which is computed by dividing the number of ways an event can happen by the total number of ways that all the events can happen. For example, in a family of two children, the probability of there being at least one girl is 75 percent, because in the listing of all the possibilities: BB, BG, GB, GG, you see that three of the choices have at least one girl. Divide 3 4 to get 0.75 or 75 percent.

The odds of there being at least one girl in a two-child family are 3 to 1 (also written 3:1). You read the odds as being three ways for the event to happen and one way for it not to happen.

Computing odds given the probability

The easiest way to compute the odds when you’re given the probability is let the probability be represented by P Percent and write: P To (100 – P) And reduce the two numbers as if they were fractions. For example, if the probability is 75 percent, you write: 75 to (100 – 75) which becomes 75 to 25. Then divide each number by 25 to get 3 to 1.

Computing probability given the odds

When you’re given the odds of an event, you need to write a fraction to compute the probability. If the odds are A To B, Write the fraction A++ ^ and then determine the decimal and the percentage. So, for example, if the odds are 4 to 1 for an event, the probability is = 5 = 0.80 = 80 percent.

Making the odds work for you

What are the odds that a person between the ages of 18 and 29 does Not Read the newspaper regularly? Did you know that someone out there has determined those odds?

The Problem: The odds that a person’s first marriage will survive without separation or divorce for 15 years are 1.3 to 1. What Percentage Of first marriages survive for 15 years?

1.3

.tVLA/V Write the fraction, 0′, , and solve for the decimal and percent.

, , = i3 . 0.5652 = 56.52 percent. That’s pretty grim. 1.3 1 2.3

The Problem: The odds that a Pokey Joe will Lose The Kentucky Derby are quoted as being 23 to 2. What is the probability that Pokey Joe will Win?

^VLA* First, rewrite the odds of winning as 2 to 23. Then write the fraction and

" ~~ 2 2

Determine the percentage. 2 + 23 = 25 = 0.08 = 8 percent. Pokey Joe has an

8 percent chance of winning. Notice what would have happened if I had com -

23 23

Puted his probability of Losing Using the 23 to 2 odds. 00 , 0 = ^7=- = 0.92 = 92

23 2 25

Percent. You then determine the probability of Winning By subtracting the 92 percent from 100 percent.

The Problem: You had 49<t (in American coins) in your pocket, but your pocket has a hole in it, and one coin fell out. If you had exactly seven coins in your pocket, what are the Odds That it was a dime that fell out?

^VLAjy First, determine what the coins are. You know that the sum of the two numbers in the odds A To B Will have to be seven, but you need more information. To have exactly 49 cents in American coins, and for there to be only 7 coins, you have to have had 1 quarter, 2 dimes, and 4 pennies (this is the only combination of seven coins that equals 49 cents). So the odds that a dime fell out are 2 to 5. Of course, this doesn’t take into account the fact that a dime is smaller than the other coins and more likely to slip through the hole.

Chapter 9