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?

Let the probability of a boy being picked when a girl is added to the nursery as x.
Adding a boy to the nursery increases the chance of a boy being picked by 50% (from 2 in whatever, to 3 in whatever) hence
The probability of a boy being picked when a boy is added is 3x/2.
A boy was picked - that's a certainty - so the probabilities sum to 1,

x + 3x/2 = 1
x=2/5

It follows that in general, the probability,x, a girl was added to a nursey, given a random selection is a boy can be found with
(n+1)/n = (1-x)/x
where n is the original number of boys.

Posted by Lee on 2003-11-05 00:57:52