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?
(In reply to re: solution - different manner of looking at this
The method I used was based on Baye's theorem, the inference of a probability of a cause from an effect. If p(A|B) represents the probability of A given that B is true, then p(A&B) = p(B)p(A|B), or p(A&B) = p(A)p(B|A).
But this is useful in considering that p(A|B) = p(A&B)/p(B). A Venn diagram is useful in seeing this, and I think relates to your leaves.
In Baye's theorem, p(A|B)=p(A&B)/p(B) = p(B|A)p(A)/p(B).
In this instance A is the birth having been that of a girl, while B is the observation of having randomly selected a boy. Further, the denominator, p(B) was broken down into two parts: p(B) = p(B|A)p(A) + p(B|~A)p(~A). Here A and ~A are each 1/2. (~ represents "not")
Posted by Charlie
on 2003-10-08 22:16:23