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a) Use Bayes' theorem and find the following:

P(good economy| prediction of good economy)

P(poor economy| prediction of good economy)

P(good economy| prediction of poor economy)

P(poor economy| prediction of poor economy)

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