A probability teaser. Suppose (as is roughly correct) that each child born is eq

Question

A probability teaser. Suppose (as is roughly correct) that each child born is equally likely to be a boy or a girl and that the sexes of successive children are independent. If we let BG mean that the older child is a boy and the younger child is a girl, then each of the combinations BB, BG, GB, GG has probability 0.25. Ashley and Brianna each have two children. (a) You know that at least one of Ashley's children is a boy. What is the conditional probability that she has two boys? (b) You know that Brianna's older child is a boy. What is the conditional probability that she has two boys?

Explanation / Answer

a)

number of comabinations with atleast one boy = 3

number of combinations that she has two boys = 1

=>

probability that she two boys given one of them is boy = 1/3

b)

number of combinations older child is boy = 2

number of combinations both are boys = 1

probability = 1/2

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