A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 30%, 20%, and 50%, respectively, of all jobs bid by the company. For i = 1, 2, 3, define Ei to be the event that a job is estimated by engineer i. The following probabilities describe the rates at which the engineers make serious errors in estimating costs:
P(error|E1) = .01, P(error|E2) = .03, and P(error|E3) = .02
a. If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 1?
b. If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 2?
c. If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 3?
d. Based on the probabilities, parts a-c, which engineer is most likely responsible for making the serious error?