I am having a terrible time with probability

Question

Specifically, the probability found in reading 8.  It's one of the few sections in the book I am genuinely defeated by, just as it was on the GMAT.  Anyways, here is one such problem that I am having difficultly with:State of economy        probability of economic state       stock performance       conditional probability stock performanceGood                             0.30                                                      Good                               0.60                                                                                                  Neutral                            0.30                                                                                                  Poor                                0.10Neutral                          0.50                                                      Good                               0.30                                                                                                  Neutral                            0.40                                                                                                  Poor                                0.30Poor                               0.20                                                     Good                               0.10                                                                                                  Neutral                            0.60                                                                                                  Poor                                0.30So here are some problems I am having a tough time figuring out:#15.)  "What is the conditional probability of having good stock performance in a poor economic environment?"The book says the answer is 0.10, so,0.10 = P(AB) / P(B)#18.) "Given that the stock had good performance, the probability the state of the economy was good is closest to?"This is a Bayes formula.  Bayes formula is:P(A | B) = [P(B | A) / P(B)] * P(A)However, when solving for the problem, the book solves for P(B | A) as (0.6)*(0.3), which seems to be the joint probability formula, not the conditional probability formula.  Why is this?

RoyD · Answer

That's the book solving for P(B|A)*P(A) not P(B|A) like you've mentioned above. P(B|A) = 0.6 and P(A) = 0.3 hence they're calculating it as 0.6*0.3