A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 20%, 30%, and 50%, respectively, of all jobs bid on by the company. For i = 1, 2, 3, define $E_i$ 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|$E_1$) =0.03, P (error|$E_2$)=0.04, and P(error|$E_3$) =0.02. Complete parts a through d.
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?
P($E_1$|error) = (Round to the nearest thousandth as needed.)
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?
P($E_2$|error) = (Round to the nearest thousandth as needed.)
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?
P($E_3$|error) = (Round to the nearest thousandth as needed.)
d. Based on the probabilities, given in parts a-c which engineer is most likely responsible for making the serious error?
Engineer (Type an integer.)