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 assumption by A)

No, no assumption was made that the boy was picked out of the group following the majority. Remembering that this is independent of the number of girls originally present, let's just take the example of the case where 4 girl babies were originally present. The following table shows on each line the original 2 boys and 4 girls followed by either boy or girl (in equal number, representing the possible newborn), and the 7 possible choices of baby to select, and whether that particular baby is a boy or a girl.

You can see that even when girls are in the majority as in this instance, out of the five times that a boy was chosen under these circumstances, two of the times it was after a girl had been born and three after a boy had been born, although in no instance would a boy have been in the majority.

boy boy girl girl girl girl; girl & chose baby 1 which is a boy
boy boy girl girl girl girl; girl & chose baby 2 which is a boy
boy boy girl girl girl girl; girl & chose baby 3 which is a girl
boy boy girl girl girl girl; girl & chose baby 4 which is a girl
boy boy girl girl girl girl; girl & chose baby 5 which is a girl
boy boy girl girl girl girl; girl & chose baby 6 which is a girl
boy boy girl girl girl girl; girl & chose baby 7 which is a girl
boy boy girl girl girl girl; boy & chose baby 1 which is a boy
boy boy girl girl girl girl; boy & chose baby 2 which is a boy
boy boy girl girl girl girl; boy & chose baby 3 which is a girl
boy boy girl girl girl girl; boy & chose baby 4 which is a girl
boy boy girl girl girl girl; boy & chose baby 5 which is a girl
boy boy girl girl girl girl; boy & chose baby 6 which is a girl
boy boy girl girl girl girl; boy & chose baby 7 which is a boy

Posted by Charlie on 2003-10-11 23:01:58