Question: Three employees of a fast food outlet, Janet, Andrea and Bill fill orders at the drive through window. Janet fills 35% of the drive through orders, Andrea 36% and Bill 29%. 93% of Janet’s orders are filled correctly as are 97% of Andrea’s and 91% of Bill’s. Suppose a drive through order is randomly selected. Find the following.

a) The probability that an order is filled by Janet and is incorrectly filled.

b) Suppose that it is known that an order is incorrectly filled. Use the tabular form of Bayes Theorem to find the probability that it is filled by Janet.

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