A construction company employs three sales engineers. Engineers 1, 2, and 3 esti

Question

A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 15%, 30%, and 55%, 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 errons in estimating costs: P (errorlE,) -0.01, P (errorlE2) -0.04, and P (errorlE3) -0.03.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 12 PlEllerror)= [ ] (Round to the nearest thousandth as needed.)

Explanation / Answer

P(E1) = 0.15

P(E2) = 0.30

P(E3) = 0.55

P(error | E1) = 0.01

P(error | E2) = 0.04

P(error | E3) = 0.03

P(error) = P(error | E1) * P(E1) + P(error | E2) * P(E2) + P(error | E3) * P(E3)

             = 0.01 * 0.15 + 0.04 * 0.3 + 0.03 * 0.55

             = 0.03

a) P(E1 | error) = P(error | E1) * P(E1) / P(error)

                      = 0.01 * 0.15 / 0.03

                      = 0.05

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