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?