An construction company employs three sales engineers. These engineers are respo

Question

An construction company employs three sales engineers. These engineers are responsible for estimating the true costs that will be involved before a company places a bid. By either serious errors by these engineers result in the company either under bidding or over bidding a contract and therefore losing money. The first engineer estimates costs on 30% of jobs and makes a serious error with probability 0.01. The second engineer estimates costs on 20% of jobs and makes a serious error with probability 0.03. The third engineer estimates costs of 50% of jobs and makes a serious error with probability 0.02. If a particular job results in a serious error, which of the engineers is most likely to be at fault? What is the probability they made the error?

Explanation / Answer

Let

E = made an error
1,2,3 = the engineer which made the error

Hence,

P(E) = P(1) P(E|1) + P(2) P(E|2) + P(3) P(E|3) = 0.30*0.01 + 0.20*0.03 + 0.50*0.02 = 0.019

Hence,

P(1|E) = P(1) P(E|1)/P(E) = 0.30*0.01/0.019 = 0.157894737

P(2|E) = P(2) P(E|2)/P(E) = 0.20*0.03/0.019 = 0.315789474

P(3|E) = P(3) P(E|3)/P(E) = 0.50*0.02/0.019 = 0.526315789

Hence, it is most probably the THIRD ENGINEER TO HAVE DONE THE ERROR. [ANSWER]

The probability that an error is made by the 3rd engineer is 0.526315789. [ANSWER]

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