Items Used in Production Process in a Factory Come from Three

Essay

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 prior probability that it came from Supplier S3? What is the posterior probability that it came from Supplier S3?