Customers are used to evaluate preliminary product designs. In the past, 91% of highly successful products received good reviews, 58% of moderately successful products received good reviews, and 11% of poor products received good reviews. In addition, 40% of products have been highly successful, 35% have been moderately successful and 25% have been poor products.

a. What is the probability that a randomly selected product attains a good review?

b. If a new product attains a good review, what is the probability that the product is indeed a highly successful product?

c. If a new product does not attain a good review, what is the probability that the product is a moderately successful product?

Step-by-step explanation:

What is given:

P (highly successful) = 0.4

P (moderate success) = 0.35

P (poor products) = 0.25

P (good review/highly success) = 0.91

P (good review/moderate success) = 0.58

P (good review/poor products) = 0.1 1

a)

P (good review) = P (highly success) * P (good review/highly success) + P (moderate success) * P (good review/moderate success) + P (poor products) * P (good review/poor products) = 0.4*0.91+0.35*0.58+0.25*0.11 = 0.364+0.203+0.0275 = 0.5945

b)

P (highly success/good review) =

P (highly success) * P (good review/highly success) / P (good review) = 0.4*0.91/0.5945=0.6123

c)

P (highly success / not good review) = P (highly success) * P (not good review / highly success) / P (not good review) = 0.4 * (1-0.91) / (1-0.6123) =

0.036/0.3877 = 0.093