A company is producing two types of ski goggles.Thirty percent of the production is of type A,and the rest is of type B.Five percent of all type A goggles are returned within 10 days after the sale,whereas only two percent of type B are returned.If a pair of goggles is returned within the first 10 days after the sale,the probability that the goggles returned are of type B is
A)0.014
B)0.140
C)0.070
D)0.483

Question

Quizplus · Accepted Answer

To find the probability that a returned pair of goggles is of type B, use Bayes' theorem. Calculate the probability of return for each type: P(Return|A) = 0.05 and P(Return|B) = 0.02. The total probability of return is P(Return) = 0.3*0.05 + 0.7*0.02 = 0.029. The probability that a returned pair is type B is P(B|Return) = (0.7*0.02) / 0.029 = 0.483.

A Company Is Producing Two Types of Ski Goggles