A college use two different textbooks during the last semester. During last semester 0.7 students used the text book by Professor B. and 0.3 students use the textbook by professor P. A survey at the end of the last semester showed that 0.4 of students who used Professor B. book were satisfied and 0.8 of students who used Professor P. were satisfied. If a student randomly selected and claims to have been satisfied with the text, what is the probability the student used Professor P. class ?
P(Satisfied and ProfP) = 0.3 * 0.8 = 0.24
That's the probability that a student has P's textbook and was satisfied, but that isn't the probability that a student that is chosen who is satisfied is using P's textbook, they're different.
You want the conditional probability, given that he is satisfied, that he used P's book.
P(P|S) = P(PintersectS) / P(S)
P(P) = .3
P(S) = .8
P(PintersectS)=.3*.8 = .24
.24 / .8 = .30