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
solution by Charlie)
I'm not sure I follow what Charlie is doing. But I come up with the same answer. Perhaps Charlie or someone else can relate these two as being the same.
Let's continue with the assumption that the probability of any given baby being a girl is 1/2.
G = the number of girls already there.
Regardless of the number of girls already there then there are two cases with equal chance of occurrence.
case 1:
the added baby is a girl.
in which case there are 2 boys (leaves on the event tree that could have led to the result), and G + 1 girls (leaves on the event tree that don't lead to the result).
case 2:
the added baby is a boy.
in which case there are 3 boys (leaves on the event tree that could have led to the result), and G girls (leaves on the event tree that don't lead to the result.)
Every leaf on this event tree is equally likely to occur, and the problem states "The selected baby is a boy", limiting it to these 5 leaves.
Of these 5 leaves, 3 of them are on a branch (case 2) where the boy was added, and 2 of them are on a branch (case 1) where the girl was added.
Again, all the leaves are equally likely to occur.
So, given that we selected a boy, in 2 of the 5 equally likely cases, a girl had been added. Therefore, 2/5.
G, the number of girls, doesn't enter into the picture.
re: solution - different manner of looking at this
