Two states of nature exist for a particular situation:

a good economy and a poor economy. An economic study may be performed to obtain more information about which of these will actually occur in the coming year. The study may forecast either a good economy or a poor economy. Currently there is a 60% chance that the economy will be good and a 40% chance that it will be poor. In the past, whenever the economy was good, the economic study predicted it would be good 80% of the time. (The other 20% of the time the prediction was wrong.) In the past, whenever the economy was poor, the economic study predicted it would be poor 90% of the time. (The other 10% of the time the prediction was wrong.)

(a) Use Bayes’ Theorem and find the following:

P1good economy  prediction of good economy2 P1poor economy  prediction of good economy2 P1good economy  prediction of poor economy2 P1poor economy  prediction of poor economy2

(b) Suppose the initial (prior) probability of a good economy is 70% (instead of 60%) and the initial probability of a poor economy is 30% (instead of 40%). Find the posterior probabilities in part (a)

based on these new values.