Exercise 2.4 (Multiplication and Total Probability Rule) Customers are used to evaluate preliminary product designs. In the past, 95 % of highly successful products, 60 % of moderately successful products, and 10 % of poor products received good review. In addition, 40% of product designs have been highly successful, 35 % have been moderately successful, and 25% have been poor products. Find the probability that a product receives a good review. Exercise 2.6 (Bayes’ Theorem) In Exercise 2.4, what is the probability that a new design will be highly successful if it receives a good review?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Exercise 2.4 (Multiplication and Total Probability Rule) Customers are used to evaluate preliminary product designs. In the past, 95 % of highly successful products, 60 % of moderately successful products, and 10 % of poor products received good review. In addition, 40% of product designs have been highly successful, 35 % have been moderately successful, and 25% have been poor products. Find the probability that a product receives a good review.

Exercise 2.6 (Bayes’ Theorem) In Exercise 2.4, what is the probability that a new design will be highly successful if it receives a good review?

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