Kookaburra Produces Its Cricket Balls in Three Different Sites: S1

Multiple Choice

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 S1?

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