Question: Three employees of a fast food outlet, Janet, Andrea and Bill fill orders at the drive through window. Janet fills 37% of the drive through orders, Andrea 32% and Bill 31%. 97% of Janet’s orders are filled correctly as are 95% of Andrea’s and 93% of Bill’s. Suppose a drive through order is randomly selected. Find the following.

a) The probability that an order is filled by Andrea. (3 points)

b) The probability that an order is correctly filled given that it is filled by Andrea. (3 points)

c) The probability that an order is filled by Andrea and is correctly filled. (6 points)

d) Suppose that it is known that an order is correctly filled. Use the tabular form of Bayes Theorem to find the probability that it is filled by Andrea. (10 points)

e) Use information above to find the probability that an order is filled by Andrea or is correctly filled. (5 points)