The Galewinds & Co. Company must decide whether it should purchase a component from a supplier or manufacture the component at its' own plant. If demand is high, it would be to the company's advantage to manufacture the component. However, if demand is low, the cost of unit manufacturing will be high due to underutilization. According to the company's current estimate the probability of low demand is about 0.34 and the probability of high demand is approximately 0.66. Then, the Galewinds & Co. Company has decided to hire a professional economic analyst who will provide additional information about demand level. Based on the analyst's past record, the company has estimated 0.83 probability that the analyst would present a favorable report given the demand is actually high, and 0.94 probability that the analyst would present an unfavorable report given the demand is actually low.

(a) If the analyst provides a favorable report (predicting high demand), how then would the Galewinds & Co. Company estimate the probability of high demand? Find the answer using the following revised probability table.

Please round the values of joint, posterior probabilities, and probability of favorable report to four decimal places.

Probability Revisions given a Favorable Report State Prior Conditional Probability Joint Posterior Probability of Probability P(Fav./State of Nature) Probability P(State of Nature/ Fav.) Nature Low High P (Favorable) = 1.0000 P (High demand | Favorable report) =Probability Revisions given an Unfavorable Report State Prior Conditional Probability Joint Posterior Probability of Probability P(Unfav./State of Nature) Probability P(State of Nature/Unfav.) Nature Low High P (Unfavorable) = 1.0000 P (High demand | Unfavorable report) = e This is not a decimal or integer value