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

Answer 1

Answer: The required probability is 0.615.

Step-by-step explanation:

Let A be the event that a product receives good reviews.

Let E₁ be the event that the product is highly successful.

Let E₂ be the event that the product is moderately successful.

Let E₃ be the event that the product is poor.

$P(E_1)=0.40\\\\P(E_2)=0.35\\\\P(E_3)=0.25\\\\P(A|E_1)=0.95\\\\P(A|E_2)=0.60\\\\P(A|E_3)=0.10$

(a) What is the probability that a product attains a good review.

So, it becomes,

$P(A)=P(E_1)P(A|E_1)+P(E_2)P(A|E_2)+P(E_3)P(A|E_3)\\\\P(A)=0.4\times 0.95+0.0.35\times 0.6+0.25\times 0.1\\\\P(A)=0.615$

Hence, the required probability is 0.615.