Nerd Pride Radio

I did not solve this problem. I was so confident in my answer and so confounded when I was told it was wrong that I didn't even attempt the math to try to sort it out. I wish I had. I don't know if I would have gotten it.

A hospital nursery contains 2 baby boys and some unknown number of baby girls. A new baby is born and placed in the nursery. Shortly after, a random baby is picked from the nursery (so this includes all the original babies and the newborn). The randomly selected baby happens to be a boy.

Given all of that, what is the probability that the newborn baby was a boy?

The counter-intuitive part: The answer is NOT 50%. There is a single, definite answer, and the problem gives you enough information to determine what that is.

Very nearly fell into trap here. First, assume that boys and girls has equal chance of being born.

Two cases.

2 boys, k+1 girls. Pr = 2/k+1+2

And

3 boys, k girls. Pr = 3/ k+3

So, probability is

2.5/k+3.

Fine.

5/2k+6

You've calculated the odds of selecting a boy at random.

Now what are the odd that the newborn is a boy given that a randomly selected baby was a boy?

[I may not have explained the problem clearly enough.]

Gah. Missed newborn part.

Something something Bayesian. Gonna need paper and pencil for this one.

3/5. That's why people hate Bayes.

My intuition would have been wholly wrong.

I figured out how explain what should have been the correct intuition from step one. Invis spell!



End invis spell.

As a check:



Just a thought.

Your final formula is dead-on for the generalized case. As the number of starting boy babies approaches infinity, the probability for this situation approaches 50%.