Students who actively participate in class are 4 times more likely to get a good grade than those who don't. 15% of students actively participate in class; 20% of students get a good grade. A person did not participate in class, what is the probability that he got a good grade?
The Attempt at a Solution
Well, I define P(G): student got a good grade; P(P): student participates. Obviously, P(G) = .2 and P(P) = .15. I also know that P(G|P) = 4P(G| not P). I am looking for the conditional probability P(G| not P). I would imagine that I need to find P(G|P) / 4, but this would mean that I need [itex] P(G \cap P) P(P) [/itex] and alas, I do not believe that I have [itex] P(G \cap P) [/itex]. ANy ideas? Anything I am missing? Thanks!