In: Statistics and Probability
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?
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