Information on previous textbooks published indicates that 10% are huge successes, 20% are modest successes, 40% break even, and 30% lost money. However, before a publishing 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.

a. What proportion of textbooks receives favorable reviews?

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

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Originally Posted by DaffyDuck23

Information on previous textbooks published indicates that 10% are huge successes, 20% are modest successes, 40% break even, and 30% lost money. However, before a publishing 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.

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a. What proportion of textbooks receives favorable reviews?

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.10*.99+.20*.70+.40*.40+.30*.20

One thing to do with a problem such as this is to build a chart. Then, you can answer any question they throw at you.

Let's assume a total of 100 for simplicity.

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                              F                              NS                    total
 
HS                        9.9                              0.1                    10

MS                        16                                24                    40

BE                        14                                6                      20 

LM                        6                                  24                    30

total                      45.9                              54.1                  100

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Look at the favorable column total. It should be the same as the solution in b. Is it?

Now, suppose they said, "what is the probability a book loses money given it has a non-favorable review?".

Go across the LM row and down the NF column and get 24/54.1=44.36%.

Just thought I would throw that in there in the event you come across problems like this.

It always helps to make a chart.