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

step-by-step explanation: