Two states of nature exist for a particular situation: a goodeconomy and a poor economy. An economic study may be performed toobtain more information about which of these will actually occur inthe coming year. The study may forecast either a good economy or apoor economy. Currently there is a 60% chance that the economy willbe good and a 40% chance that it will be poor. In the past, whenever the economy was good, the economic study predicted it would begood 80% of the time. (The other 20% of the time the prediction waswrong.) In the past, whenever the economy was poor, the economicstudy predicted it would be poor 90% of the time. (The other 10% ofthe time the prediction was wrong.)
(A) Use Bayes’ theorem and find thefollowing:
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 ofa good economy is 70% (instead of 60%), and the probability of apoor economy is 30% (instead of 40%). Find the posteriorprobabilities in part a
based on these new values.
