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 S2?
A) 50%.
B) 47.6%.
C) 28.6%.
D) 23.8%.

Question

Quizplus · Accepted Answer

P(S2|D) = P(D|S2) * P(S2) / P(D)= 0.02 * 0.3 / (0.05 * 0.2 + 0.02 * 0.3 + 0.01 * 0.5)= 0.006 / 0.009= 0.2857= 28.57%

Kookaburra Produces Its Cricket Balls in Three Different Sites: S1