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

Question

A construction company employs three sales engineers. Engineers 1,2and 3 estimate the costs of 35%, 20%, and 45%, respectively, of all jobs bid by the company. For k=1, 2, 3, define Ak to be the event that a job is estimated by engineer k, define E to be the event that a serious error is made in estimating the cost. The following probabilities are known to describe the error rates of the engineers : P(E|A1)=0.01, P(E|A2)=0.04, P(E|A3)=0.02, If a particular bid results in a serious error in estimating the job cost, which engineers is most likely possible?

Explanation / Answer

P(A1) = 0.35

P(A2) = 0.2

P(A3) = 0.45

P(Ak | E) = P(E | Ak) * P(Ak) /P(E) where k = 1,2,3

So, for which Engineer P(E | Ak) * P(Ak) is more, that engineer is most likely possible.

So, for, k = 1, P(E | Ak) * P(Ak) = 0.01 * 0.35 = 0.0035

So, for, k = 2, P(E | Ak) * P(Ak) = 0.04 * 0.2 = 0.008

So, for, k = 3, P(E | Ak) * P(Ak) = 0.02 * 0.45 = 0.009

So, engineer 3 is most likely possible.

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