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 60% chance that the economy will be good and a 40% chance that the economy 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 90% of the time.(The other 10% of the time the prediction was wrong.)

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.

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩