The editor of a textbook publishing company is deciding whether to publish a proposed textbook. Information on previous textbooks published show that 20 % are huge successes, 30 % are modest successes, 30 % break even, and 20 % are losers. Before a decision is made, the book will be reviewed. In the past, 99 % of the huge successes received favorable reviews, 70 % of the moderate successes received favorable reviews, 40 % of the break-even books received favorable reviews, and 20 % of the losers received favorable reviews. If the textbook receives a favorable review, what is the probability that it will be huge success?

34.86% probability that it will be huge success

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Receiving a favorable review.

Event B: Being a huge success.

Information on previous textbooks published show that 20 % are huge successes

This means that

99 % of the huge successes received favorable reviews

This means that

Probability of receiving a favorable review:

20% are huge successes. Of those, 99% receive favorable reviews.

30% are modest successes. Of those, 70% receive favorable reviews.

30% break even. Of those, 40% receive favorable reviews.

20% are losers. Of those, 20% receive favorable reviews.

Then

Finally

34.86% probability that it will be huge success

step-by-step explanation: