A construction company employs three sales engineers Enginee

A construction company employs three sales engineers. Engineers 1,2, and 3 estimate the costs of 15%, 25%, and 60%, respectively, of all jobs bid on by the company. For i = 1,2,3, define Ej 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: PCerrorlEj) - 0.01, P(error|E2) - 0.02, and P(error|E3) = 0.03.

Solution

Note that

P(error) = P(E1) P(error|E1) + P(E2) P(error|E2) + P(E3) P(error|E3) = 0.15*0.01+0.25*0.02+0.60*0.03

P(error) = 0.0245

a)

P(E1|error) = P(E1) P(error|E1) / P(error) = 0.15*0.01/0.0245 = 0.06122449

= 0.061 [answer]

b)

P(E2|error) = P(E2) P(error|E2) / P(error) = 0.25*0.02/0.0245 = 0.204081633

=0.204 [answer]

c)

P(E3|error) = P(E3) P(error|E3) / P(error) = 0.60*0.03/0.0245 = 0.734693878

= 0.735 [answer]

d)

ENGINEER 3. [ANSWER]