Question: Three employees of a fast food outlet, Janet, Andrea and Bill fill orders at the drive through window. Janet fills 29% of the drive through orders, Andrea 36% and Bill 35%. 2% of Janet’s orders are filled incorrectly as are 2.5% of Andrea’s and 3% of Bill’s. Suppose a drive through order is randomly selected. Find the following.

a) The probability that an order is filled by Andrea

b) The probability that an order is correctly filled given that it is filled by Bill

c) The probability that an order is filled by Bill and is correctly filled.

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 Bill.

e) Use information above to find the probability that an order is filled by Bill or is correctly filled.