A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of typeB. 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).014.
B).140.
C).070.
D).483.

Question

Quizplus · Accepted Answer

The probability that a returned pair of goggles is of type B can be calculated using Bayes' theorem. Let's denote $P(A)$ as the probability of producing type A goggles, $P(B)$ as the probability of producing type B goggles, $P(R|A)$ as the probability of type A goggles being returned, and $P(R|B)$ as the probability of type B goggles being returned. We want to find $P(B|R)$, the probability that a returned pair of goggles is of type B.Given:- $P(A) = 0.30$- $P(B) = 0.70$ (since 100% - 30% = 70%)- $P(R|A) = 0.05$- $P(R|B) = 0.02$The probability that a pair of goggles is returned, $P(R)$, can be calculated as:$$P(R) = P(R|A)P(A) + P(R|B)P(B) = 0.05 \times 0.30 + 0.02 \times 0.70 = 0.029$$Using Bayes' theorem, the probability that a returned pair of goggles is of type B, $P(B|R)$, is:$$P(B|R) = \frac{P(R|B)P(B)}{P(R)} = \frac{0.02 \times 0.70}{0.029} \approx 0.483$$Therefore, the correct answer is D, which is approximately 0.483.

A Company Is Producing Two Types of Ski Goggles