The Chocolate House specializes in hand-dipped chocolates for special occasions.
ID: 3238609 • Letter: T
Question
The Chocolate House specializes in hand-dipped chocolates for special occasions. Three employees do all of the product packaging. Clerk 1 packs 33% of the chocolate boxes, Clerk 2 packs 23% of the chocolate boxes, and Clerk 3 packs 44% of the chocolate boxes. Sometimes defective chocolates are packaged in the boxes. If Clerk 1 does the packing, the defective box rate is 2%. If Clerk 2 does the packing, the defective box rate is 2.5%. If Clerk 3 does the packing, the defective box rate is 1.5%.
Use a probability tree to answer the following questions:
(Round all intermediate and final calculations to four decimals)
a) What's probability that a randomly selected box of chocolates was packed by Clerk 2 and does not contain any defective chocolate?
b) What is the probability that a randomly selected box contains defective chocolate?
c) Suppose a randomly selected box of chocolates is defective. What is the probability that it was packaged by Clerk 3?
Explanation / Answer
a) P(Packed by clerk 2 and does not contain any defective chocolate)
= 0.23*(1 - 0.025)
= 0.2243
b) P(Defective Chocolate)
= 0.33*0.02 + 0.23*0.025 + 0.44*0.015
= 0.0190
c) P(Clerk 3 | Defective)
= P(Clerk 3 and defective) / P(Defective)
= (0.44*0.015) / 0.0190
= 0.3474