# Probability doubt

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## Probability doubt

 It is now generally accepted that cigarette smoking causes heart disease, lung cancer, and many other diseases. However, in the 1950s this idea was controversial. There was a strong association between smoking and ill-health, but association is not causation. R. A. Fisher advanced the "constitutional hypothesis:" there is some genetic factor that disposes you both to smoke and to die. To refute Fisher's idea, the epidemiologists used twin studies. They identified sets of smoking-discordant monozygotic twin pairs. ("Monozygotic" twins come from one egg and have identical genetic makeup; "smoking-discordant" means that one twin smokes, the other doesn't.") Now there is a race. Which twin dies first, the smoker or the non-smoker? Data from a Finnish twin study are shown below. Data from Finnish twin study                                                  Smokers        Non smokers All Causes                                       17                   5 Coronary heart disease                       9                    0 Lung cancer                                     2                    0 According to the first line of the table, there were 22 smoking-discordant monozygotic twin pairs where at least one twin of the pair died. In 17 cases, the smoker died first; in 5 cases, the non-smoker died first. According to the second line, there were 9 pairs where at least one twin died of coronary heart disease; in all 9 cases, the smoker died first. According to the last line, there were 2 pairs where at least one twin died of lung cancer, and in both pairs the smoker won the race to death. (Lung cancer is a rare disease, even among smokers) For parts (a-c), suppose that each twin in the pair is equally likely to die first, so the number of pairs in which the smoker dies first is like the number of heads in coin-tossing. (a) ON this basis, what is the chance of having 17 or more pairs out of 22 where the smoker dies first? (b) Repeat the test in part (a), for the 9 deaths from coronary heart disease. (c) Repeat the test in part (a), for the 2 deaths from lung cancer. (d) Can the difference between the death rates for smoking and non-smoking twins be explained by      (i) chance?      (ii) genetics?      (iii) health effects of smoking?
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## Re: Probability doubt

 Hi Technoazhar, This is a simple binomial problem, X ~ bin(n,p) a) n = 22, p = 0.5, you have to find P(X>= 17) Now give the other parts a try.
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## Re: Probability doubt

 Hey Prerna! Thanks for your candor. You helped me get over the doubt. However, I am especially doubtful about the part (d) of the question. Give it a try. :-)