The editor of a textbook publishing company is trying to decide whether to publi

Question

The editor of a textbook publishing company is trying to decide whether to publish a proposed business statistics textbook. Information on previous textbooks published indicate that 20 %20% are huge successes, 30 %30% are modest successes, 40 %40% break even, and 10 %10% are losers. However, before a publishing decision is made, the book will be reviewed. In the past, 97 %97% of the huge successes received favorable reviews, 60 %60% of the moderate successes received favorable reviews, 40 %40% of the break-even books received favorable reviews, and 30 %30% of the losers received favorable reviews. Complete parts (a) and (b).

a- the proposed textbook receives a favorable review, how should the editor revise the probabilities of the various outcomes to take this information into account?

The probability that if the proposed textbook receives a favorable review, the book will be a huge success is

b-What proportion of textbooks receives favorable reviews?

Explanation / Answer

Let H shows the event that book get huge successes, M shows the event that book get modest successes, B shows the event that book get break even and L shows the losers. So

P(H) = 0.20, P(M) = 0.30, P(B) = 0.40, P(L) = 0.10

Let F shows the event that book get favorable review. So

P(F|H) = 0.97, P(F|M) = 0.60, P(F|B) = 0.40, P(F|L) = 0.30

By the law of total probability, the probability that textbooks receives favorable reviews is

P(F) = P(F|H)P(H) + P(F|M)P(M) + P(F|B)P(B) + P(F|L)P(L) = 0.97 * 0.20 + 0.60 * 0.30 + 0.40 *0.40 + 0.30 *0.10 = 0.194 + 0.18 + 0.16 + 0.03 = 0.564

(a)

The probability that if the proposed textbook receives a favorable review, the book will be a huge success is

P(H|F) = [ P(F|H) P(H) ] / P(F) = 0.194 / 0.564 = 0.344

The probability that if the proposed textbook receives a favorable review, the book will be a modest success is

P(M|F) = [ P(F|M) P(M) ] / P(F) = 0.18 / 0.564 = 0.319

The probability that if the proposed textbook receives a favorable review, the book will be a break even success is

P(B|F) = [ P(F|B) P(B) ] / P(F) = 0.16 / 0.564 = 0.284

The probability that if the proposed textbook receives a favorable review, the book will be a loser is

P(L|F) = [ P(F|L) P(L) ] / P(F) = 0.03 / 0.564 = 0.053

(b)

The proportion of textbooks receives favorable reviews is

P(F) = P(F|H)P(H) + P(F|M)P(M) + P(F|B)P(B) + P(F|L)P(L) = 0.97 * 0.20 + 0.60 * 0.30 + 0.40 *0.40 + 0.30 *0.10 = 0.194 + 0.18 + 0.16 + 0.03 = 0.564

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