Question: 11.33 A probability teaser. Suppose (as is roughly correct) that each child born is equally likely to be a boy or a girl and that

11.33 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 BO mean that the older child is a boy and the younger child is a girl, then each of the combinations BB, BO, 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?

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