Math Help - conditional probability

Hi,

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.

Originally Posted by kkoutsothodoros

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.

There is no flaw in your reasoning.

The answer is . Why do you think that it is not?

Hi thanks! the book specifically gives the hint: "the answer is not 12/22!" but it's what i get!! i've done this before. i guess i should be a little more confident in my logic.

Originally Posted by kkoutsothodoros

Hi thanks! the book specifically gives the hint: "the answer is not 12/22!" but it's what i get!! i've done this before. i guess i should be a little more confident in my logic.

Are you sure that you have copied the question exactly?

If it were given that student is from Able's class, what is the probability it is a girl? That would be different.

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!