I am working on this problem: There are two precalculus sections at West High School. Mr. Abel's class has 12 girls and 8 boys, while Mr. Bonitz's class has 10 girls and 15 boys. If a West High precalculus student chosen at random happens to be a girl, what is the probability she is from Mr. Abel's class? [the answer is not 12/22].
My reasoning is as follows:
P(A|G) = P(G|A)*P(A)/P(G) = (12/20)*(20/45)/(22/45) which is, unfortunately, giving me 12/22. i don't see any flaws in my reasoning. Can someone look over this. thanks in advance.
Thanks again. The answer in the back of the book is 3/5 which agrees with your last comment. i'm a math tutor and i used to be an actuary so conditional probability is something I've thought about often. when i got 12/22 and the problem specifically stated it WASN'T it was a bit embarrassing!