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 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?

Answer 1

Answer:

Step-by-step explanation:

The given information can be tabulated as follows.

Success type          High             Moderate              Low            Total

                                 0.40                   0.35                 0.25             1

Good reviews          0.95                    0.60                0.10

Combined prob       0.4*0.95             0.35*0.6          0.25*0.1

                                 0.38                    0.21                  0.025       0.6125

A) the probability that  a product attains a good review

=Prob it it successful and gets good review + Prob it  is moderate successful and gets good review +Prob it it low successful and gets good review

= 0.6125

B) If a new design attains a good review,  the probability that it will be a highly successful product= $\frac{0.38}{0.6125} \\=0.6204$

C) Prob that does not attain a good review =(0.40*0.05)+0.35(0.4) +(0.25)*0.9

= 0.385

Prob for successful not getting good review = 0.40(0.05) = 0.02

Reqd prob = $\frac{0.02}{0.385} \\=0.05195$