You are the owner of a company that produces a product your

You are the owner of a company that produces a product. your customers are used to evaluate new preliminary product designs. In the past, 95% of highly successful new products recieved good reviews, 60% of moderately successful products recieved good reviews and 10% of poor products recieved good reviews. In addition, 40% of new products produced by your company have been highly successful, 35% have been moderately successful and 25% have been poor products.

a) What is the probability that a new product attains a good review

b) If a new product attains a good review, what is the probability that it will be highly successful?

Solution

Let

H, M, P = highly, moderately, and poorly successful
G = goof review

a)

P(G) = P(H) P(G|H) + P(M) P(G|M) + P(P) P(G|P)

P(G) = 0.40*0.95 + 0.35*0.60 + 0.25*0.10 = 0.615 [ANSWER]

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b)

P(H|G) = P(H) P(G|H) / P(G) = 0.40*0.95/0.615 = 0.617886179 [ANSWER]