An investment advisor recommends the purchase of shares in Probaballisitics, Inc. He has made the following predictions:

P(Stock goes up 20% | Rise in GDP) = .6
P(Stock goes up 20% | Level GDP) = .5
P(Stock goes up 20% | Fall in GDP) = .4

An economist has predicted that the probability of a rise in the GDP is 30%, whereas the probability of a fall in the GDP is 40%.

a. What is the probability that the stock will go up 20%?
b. We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP?