For U.S. live births, P(boy) and P(girl) are approximately 0.51 and 0.49, respectively.a According to a newspaper article, a medical process could alter the probabilities that a boy or a girl will be born. Researchers using the process claim that couples who wanted a boy were successful 85% of the time, while couples who wanted a girl were successful 77% of the time.b Assuming that the medical process does have an effect on the sex of the child:
a. Without medical intervention, what is the probability of having a boy?
b. With medical intervention, what is the conditional probability that a couple who wants a boy will have a boy?
c. With medical intervention, what is the conditional probability that a couple who wants a girl will have a girl?