Advanced statistics question..?

Suppose that a disease is transmitted via a dominant mode of inheritance and that one parent is affected and the other is not. The probability then that any particular offspring will get the disease is ½.


a) What is the probability that in a family with 2 children, both are affected?





b) What is the probability that exactly 1 is affected?





c) What is the probability that neither child is affected?

Advanced statistics question..?
every child is independent of the other with respect to getting the disease.





1/2 prob the first child has the disease, 1/2 prob the second does, the prob both have the disease is thus:


1/2 * 1/2 = 1/4





to have exactly one effect you have 1/2 * 1/2 that this first is affected and the second is not plus the 1/2 * 1/2 prob that the first is not but the second child is: 1/2 * 1/2 + 1/2 * 1/2 = 1/2





there is a 1/4 prob that neither child has the disease. this is the same logic as part 1.
Reply:a. (1/2)(1/2) = 1/4


b. (1/2)(1-1/2) + (1-1/2)(1/2) = (1/4) + (1/4) = 1/2


c (1-1/2)(1-1/2) = (1/2)(1/2) = 1/4

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