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?

Answer 1

Answer:

Step-by-step explanation:

given that the Chocolate House specializes in hand-dipped chocolates for special occasions. Three employees do all of the product packaging

Clerk          I           II           III    total

   

Pack      0.33          0.23    0.44 1

   

Defective 0.02 0.025    0.015  

   

Pack&def 0.0066 0.00575 0.0066 0.01895

a)  probability that a randomly selected box of chocolates was packed by Clerk 2 and does not contain any defective chocolate

= P(II clerk) -P(II clerk and defective) = $0.23-0.00575=0.22425$

b) the probability that a randomly selected box contains defective chocolate=P(I and def)+P(ii and def)+P(iiiand def)

=0.01895

c) Suppose a randomly selected box of chocolates is defective. The probability that it was packaged by Clerk 3

=P(clerk 3 and def)/P(defective)

=$\frac{0.0066}{0.01895} \\=0.348285$