Question

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?

Answer 1

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.