Errors in estimating job costs. 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 on 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:

P1error 0E12 = .01, P1error 0E22 = .03, and P1error 0E32 = .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 given in parts a–c, which engineer is most likely responsible for making the serious error?