Question

A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.4, 0.35 and 0.25 respectively. From past experience it is known that the probability of cost overruns for the firms are 0.05, 0.03, and 0.15, respectively.
a. Suppose a cost overrun is experienced by the company. What is the probability that the consulting firm involved is company A?

b. Are the events selecting company A, and incurring in cost overruns independent?

Answer 1

Answer:

(a) 0.29412 .

(b) No, the events selecting company A and incurring in cost overruns are not independent.

Step-by-step explanation:

We are given that a certain federal agency employs three consulting firms (A, B and C) with probabilities 0.4, 0.35 and 0.25 respectively i.e.;

 P(A) = 0.4        P(B) = 0.35          P(C) = 0.25

Also, From past experience it is known that the probability of cost overruns for the firms are 0.05, 0.03, and 0.15, respectively which means;

Let CO = Event of cost overruns

P(CO/A) = 0.05 - It means probability of cost overruns given the consulting firm involved was A.

Similarly, P(CO/B) = 0.03      P(CO/C) = 0.15

(a) Probability that the consulting firm involved is company A given a cost overrun is experienced by the company is given by, P(A/CO);

We will use Bayes' theorem here calculating the above probability ;

           P(A/CO) = $\frac{P(A)*P(CO/A)}{P(A)*P(CO/A) + P(B)*P(CO/B) + P(C)*P(CO/C)}$

                          = $\frac{0.4*0.05}{0.4*0.05 + 0.35*0.03 + 0.25*0.15}$ = 0.29412 .

(b) No, the events selecting company A and incurring in cost overruns are not independent because the cost overruns happens only when the consulting firm is involved and also the cost overruns will differ as we move towards another consulting firm so the chances of cost overruns will depend on the fact that which consulting firm has been involved.