Question

Customers are used to evaluate preliminary product designs. In the past 95% of highly successful products received good reviews, 60% of moderately successful products received good reviews, and 10% 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 product receives a good review?

b. If a product receives a good review, what is the probability that it will be a highly successful product?

c. If a product does not receive a good review, what is the probability that it will be a highly successful product?

Answer 1

P(   highly success   ) =    0.4
P(   moderate success   ) =    0.35
P(    poor products   ) =    0.25
  
P(   good review   | highly success)=   0.95
P(   good review   | moderate success)=   0.6
P(   good review   | poor products)=   0.1

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*0.95+0.35*0.6+0.25*0.1=               0.615

b)

P(highly success| good review) = P(highly success)*P(good review| highly success)/P(good review)=               0.4*0.95/0.615=       0.6179

c)

P(highly success| not good review) = P(highly success)*P(not good review| highly success)/P(not good review)=0.4*(1-0.95)/(1-0.615)=   0.0519