Customers are used to evaluate preliminary product designs. In the past, 94% of

Question

Customers are used to evaluate preliminary product designs. In the past, 94% of highly successful products received good reviews, 59% of moderately successful products received good reviews, and 13% 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. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that a product attains a good review? (b) If a new design attains a good review, what is the probability that it will be a highly successful product? (c) If a product does not attain a good review, what is the probability that it will be a highly successful product?

Explanation / Answer

Ans:

a)P(good reviews)=0.94*0.4+0.59*0.35+0.13*0.25=0.615

b)P(highly successful/good reviews)=P(good reviews/highly successful)*P(highly successful)/P(good reviews)

=(0.94*0.4)/0.615=0.611

c)P(highly successful/not good reviews)=P( not good reviews/highly successful)*P(highly successful)/P( not good reviews)

=(1-0.94)*0.4/(1-0.615)

=0.06234

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