Answer to Question #4526 in Statistics and Probability for lucki

Question #4526
The Chocolate House specializes in hand-dipped chocolates for special occasions. Recently, several long-time customers have complained about the quality of the chocolates. It seems there are several partially covered chocolates in each box. The defective chocolates should have been caught when the boxes were packed. The manager is wondering which of the three packers is not doing the job properly. Clerk 1 packs 40% of the boxes and usually has a 2% defective rate. Clerk 2 packs 30% with a 2.5% defective rate. Clerk 3 boxes 30% of the chocolates and her defective rate is 1.5%. Which clerk is most likely responsible for the boxes that raised the complaints?
Expert's answer
P(clerk1|defective)= (0.02)(0.4)/(0.02)= 0.4
P(clerk2|defective)= (0.025)(0.3)/(0.02)= 0.375
P(clerk3|defective)= (0.015)(0.3)/(0.02)= 0.225
Therefore clerk 1 has the highest probaility, thus most likely to be responsible for the boxes that raised complaints.

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