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2 years ago

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The editor of a textbook publishing company is deciding whether to publish a proposed textbook. Information on previous textbook

s 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?

1 answer:

kogti [31]2 years ago

4 0

Answer:

34.86% probability that it will be huge success

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

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 $P(B) = 0.2$

99 % of the huge successes received favorable reviews

This means that $P(A|B) = 0.99$

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

$P(A) = 0.2*0.99 + 0.3*0.7 + 0.3*0.4 + 0.2*0.2 = 0.568$

Finally

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.2*0.99}{0.568} = 0.3486$

34.86% probability that it will be huge success

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So we are eliminating 3rd choice now.

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I was looking at the rows as if they were choices.

Let me break up my choices.

So we said $x=-\frac{7\pi}{6}$ doesn't work because it is not included in the inequality $0\le x \le 2\pi$ .

How about $x=0$ ? This leads to $\csc(0)$ which doesn't exist because $\sin(0)=0$ .

So neither of the first two choices on the first row.

Let's look at the second row again.

We said $\frac{\pi}{4}$ worked but not $\frac{\pi}{2}$

Let's look at the choices on the third row.

We said $\frac{5\pi}{6}$ worked but not $x=\pi$

Let's look at at the last choice.

We said it gave something less than 1 so this choice doesn't work.

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2 years ago

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