Two states of nature exist for a particular situation: a good economy and a poor economy....

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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 Bayesâ€™ 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.

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Probability of good economy Pgood 060Probability of poor economy Ppoor 040Probability of prediction of good economy given that economy wasgood PPGgood 08Probability of prediction of poor See Answer

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