A certain federal agency employs 3 consulting firms (A, B andC) with probailites

Question

A certain federal agency employs 3 consulting firms (A, B andC) with probailites 0.4, 0.35 and 0.25 respectively. from pastexperience it is known that the probability of cost overruns forthe firms are 0.05, 0.03 and 0.15 respectively a) what is the probability that a cost overrun will beexperienced by the agency b) Suppose a cost overrun is experienced by the agency. Whatis the probability that the firm involved in company C A certain federal agency employs 3 consulting firms (A, B andC) with probailites 0.4, 0.35 and 0.25 respectively. from pastexperience it is known that the probability of cost overruns forthe firms are 0.05, 0.03 and 0.15 respectively a) what is the probability that a cost overrun will beexperienced by the agency b) Suppose a cost overrun is experienced by the agency. Whatis the probability that the firm involved in company C

Explanation / Answer

Given that there is an overrun, the probability that it was dueto firm x is the product pxqx normalizedby the total probability of there being an overrun (since we knowthere is one). That is,

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