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(2): I have not read Charlie's post yet by FatBoy)
FatBoy,
Don't misunderstand the problem.
Even with the problem as stated. For any given birth, the likelihood that a girl is added to the nursery versus a boy being added is 50% (our assumption for the calculation).
Whether or not we select a baby at random, after the fact, doesn't change that likelihood.
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A different example that may help this is... what if we selected a baby at random 10000 times (with replacement) afterwards.
Assuming there are fewer than, say, 20 babies in the nursery, we will likely come up with a VERY close approximation to the actual ratio of babies in the nursery. If we further know there had been only 2 boys in there initially, we could almost definitively (with a high degree of accuracy) state whether the last baby added had been a third boy or another girl!
It still doesn't change the fact that, independently, the likelihood of adding a boy versus adding a girl is 50/50.
In other words, doing random sampling afterwards, tells us something about what happened earlier.
re(3): I have not read Charlie's post yet
