Kookaburra produces its cricket balls in three different sites: S1, S2 and S3. S1 provides 20%, S2 provides 30% and S3 provides 50% of all balls. However, S1 produces 5% (0.05) defective items, S2 produces 2% (0.02) while S3 produces 1% (0.01). If an item sampled at random was found to be defective, what is the POSTERIOR probability it came from S3?
A) 50%.
B) 47.6%.
C) 28.6%.
D) 23.8%.

Question

Quizplus · Accepted Answer

The posterior probability that a defective ball came from S3 can be calculated using Bayes' theorem. The probability of a ball being defective from S3 is 0.5 * 0.01 = 0.005. The total probability of a ball being defective is (0.2 * 0.05) + (0.3 * 0.02) + (0.5 * 0.01) = 0.019. Thus, the posterior probability is 0.005 / 0.019 = 0.263, which is approximately 26.3%, closest to 23.8%.

Kookaburra Produces Its Cricket Balls in Three Different Sites: S1