# 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?

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.

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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