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 indicates that 8% are huge successes, 12% are modest successes, 40% break even, and 40% are losers. However, before a publishing decision is made, the book will be reviewed. In the past, 90% of the huge successes received favorable reviews, 70% of the moderate successes received favorable reviews, and 40% of the break-even books received favorable reviews, and 20% of the losers received favorable reviews.

(a) What proportion of textbooks receive favorable reviews?

(b) If the proposed textbook receives a favorable review, how should the editor revise the

probabilities of the various outcomes to take this information into account?

Answer 1

a) 39.6%

b) See suggestion below

Explanation:

a)

Since a book can only have one classification (huge or modest success, break even or loser) the sets are disjoint, so the proportion of textbooks that receive favorable reviews is the sum of the proportions for each category

8% of 90% + 12% of 70% + 40% of 40% + 40% of 20% =

0.08*0.9 + 0.12*0.7 + 0.4*0.4 + 0.4*0.2 = 0.396 = 39.6%

b)

The editor should now revise the following conditional probabilities

Probability that the book is a huge success given that it received a favorable review.

Probability that the book is a moderate success given that it received a favorable review.

Probability that the book is a break even given that it received a favorable review.

Probability that the book is a loser success given that it received a favorable review.

To compute these probabilities he needs the Baye's Theorem on conditional probabilities.