Items used in production process in a factory come from three suppliers S1, S2 and S3. S1 provides 20%, S2 provides 30% and S3 provides 50%. 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 approx. posterior probability it came from Supplier S1?
A) 48%.
B) 20%.
C) 5%.
D) 21%.

Question

Quizplus · Accepted Answer

Using Bayes' theorem, the posterior probability that a defective item came from S1 is calculated as: P(S1|D) = [P(D|S1) * P(S1)] / [P(D|S1) * P(S1) + P(D|S2) * P(S2) + P(D|S3) * P(S3)]. Substituting the given values: P(S1|D) = [0.05 * 0.20] / [0.05 * 0.20 + 0.02 * 0.30 + 0.01 * 0.50] = 0.01 / 0.0208 ≈ 0.48 or 48%.

Items Used in Production Process in a Factory Come from Three