Bayes theory interview question.

[ntyris9]

This question is a typical interview question at a job I am currently seeking. The reason I am posting it is I have had different answers from various individuals all who have some credibility.

You know there are 2 boys and an unknown number of girls in a nursery at a hospital. Then a woman gives birth a baby, but you dont know its gender, and it is placed in the nursery. Then a nurse comes in a picks up a baby and it is a boy. Given that the nurse picks up a boy, what is the probability that the woman gave birth to a boy? (Hint, it does not matter how many girls are in the nursery to begin with)

I am under the impression you must you bayes theory for this if that is incorrect please correct me. I would appreciate explaining the problem thank you very much.

[Mike Z.]

I agree with using Bayes theory.

Try drawing a tree diagram and tell us what you get.

[ntyris9]

Mike,

Drew a tree diagram assuming there were ten girls in the nursery to begin with since problem said it did not matter. I ended up computing (3/26)/(5/26) which gave me 3/5 which intuitively sounds correct and had been a suggested answer. I must admit doing the tree diagram is what gave me this solution. I thank you very much for giving me the satisfaction of solving the problem myself (if I am in fact correct haha).

I was wondering though is there a mental approach I should be taking to this type of problem where I do not need to make up a number of girls? I was not a stat major so I have been honing my skills in preparation for an interview and very much want to think mentally in a "Bayesnian way".

Again thank your for you help.

[Mike Z.]

3/5 is correct.

You could let n stand for the number of girls originally in the nursery, and get the same kind of cancellation.