The Boy Girl Paradox

[samsoneffect]

So this post comes via my younger brother, who directed me to this thread on the Something Awful Forums, which after some time devolves into arguing about how probability works with respect to the particular problem. My aim here is to point out the problem, and elucidate the proper solution. So without further ado, I present to you the Boy or

Comments

[thaft]

I would never have even considered that there was a 2/3 probability. That doesn't make any sense to me.

On a similar topic, I read a neat article a couple days ago about how doctors are becoming increasingly innumerate because theoretically because admission to med school has become a craft, as opposed to an art. People take exactly the classes that the need for admission, and don't take any chance (GPA-wise) on the rest.

Anyway, the article cited a study among doctors. It goes as follows:

A woman tests positive for breast cancer. She asks you if she has breast cancer, or what her chances of having breast cancer are.

You, as her very intelligent, handsome GP know the following is true:

1) The probability that a woman has breast cancer is 1%
2) If a woman has breast cancer, the probability that she tests positive is 90%.
3) If a woman does not have breast cancer, the probability that she nonetheless tests positive is 9%.

What is the best answer to the patient's question?

a) The probability that she has breast cancer is about 81%
b) Out of 10 women with a positive mammogram, about 9 have breast cancer.
c) Out of 10 women with a positive mammogram, about 1 has breast cancer.
d) The probability that she has breast cancer is about 1%

In the study, 60% of the physicians answered a) or b). Only 21% answered correctly - C.

I think the trouble is, statistics are pretty straightforward if you go into it with an open mind and just work through it, but a lot of people see MATH and shut down.

[cosineoflove]

Hmm, will try to get back to you after I take c&o :)

also, I like the med school question, thaft :)