3) A company can lose its bid for an oilfield lease due if there is a calculatio

Question

3) A company can lose its bid for an oilfield lease due if there is a calculation error in the project economics. Such calculations are performed by one of three executives in the company A, B or C. On the basis of past performance, it is known that the probability that A would make a mistake is 0.001, the probability that B would do so is 0.002, and the probability that C would make the mistake is 0.001. A is responsible for calculating the project economics is 50% of the project bids, while B and C split the rest of the cases. If a company lost a bid because of calculation error, what is the probability that the calculation was performed by A?

Explanation / Answer

As per Bayes theorem:

P(A calculated/Lost a Bid) = P(Lost a bid/A calculated) P(A calculated) / [P(Lost a Bid /A calculated) P(Acalculated)+ P(Lost a Bid /B calculated) P(B calculated)+ P(Lost a Bid/C calculated) P(C calculated)]

Given P (A calculated) = 0.5 , P (B calculated) = 0.25 and P (C calculated) =0.25

P(A calculated/Lost a Bid) = (0.001 *0.5) / (0.001*0.5+0.002*0.25+0.001*0.25)

=0.4

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