Question

A certain federal agency employs three consulting firms (A, B, and C) with probabilities 0.350, 0.40, and 0.25, respectively. From past experience it is known that the probabilities of cost overruns for the firms are 0.05, 0.25, and 0.15, respectively. (a) What is the probability of cost overrun? (b) Suppose a cost overrun is experienced by the agency. What is the probability that the consulting firm involved is company C?

Answer 1

Hello Sir/ Mam

Let A be the event that the certain federal agency employs firm A.

Let B be the event that the certain federal agency employs firm B.

Let C be the event that the certain federal agency employs firm C.

Let O be the event of cost overrun.

Hence, using given probabilities:

(a)

(b)

I hope this solves your doubt.

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