to determine the probability that a person who fails the test actually has the disease.

5.86 . to determine the probability that a person who fails the test actually has the disease. Alice, Bill, and Charley (who can be labeled A, B, and C) are employees of a fast- food restaurant, taking orders from customers at a counter. From prior observation, we know that A makes mistakes 1 time in 100, B makes mistakes 3 times in 10 and C makes mistakes 5 times in 100. A, B, and C take 50%, 30%, and 20% ofthe orders. If the manager finds that a mistake, M, has been made in a certain order what are the probabilities that the order was filled by A, B, or C?