A baby is added to a hospital nursery. Before the baby was added there were two boys in the nursery and an uncounted number of girls. After the new baby is added a baby is selected at random among all the babies. The selected baby is a boy.
What is the probability that the added baby was a girl?
What we want is prob(Girl added(G)|Boy was picked(X))?
Define:
Number of babies after the addition = N
Girl added = G
Boy added = B
Boy Picked = X
Prob(G|X) = Prob(G intersect X)/ {Prob(G intersect X) + Prob(B intersect X)}
= (2/N) / (2/N + 3/N) = 2/5 = .40
Bayes Theorem
