Question

A certain agency employs two consulting firms (A and B) with probabilities 0.60 and 0.4, respectively. From past experience, it is known that the probability of cost overruns (wal you will) for the firms is 0.05 and 0.1, 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 B2

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Abdul-Rahim Taysir

Answer 1

1.

{P(cost overruns given firm A) = 0.05

P(cost overruns given firm B) = 0.1}

P( cost overruns)

= P(firm A employed) * P(cost overruns given firm A) + P(firm B employed) * P(cost overruns given firm B)

= 0.6 * 0.05 + 0.4 * 0.1

= 0.03 + 0.04

= 0.07

2.

P(consulting firm involved is company B given agency has experienced cost overrun)

{Let A be event that company experienced cost overrun

C is event that consulting firm B is involved}

= P(C | A)

Using Bayes theorem,

= P(A|C) * P(C) / P(A)

= 0.1 * 0.4 / 0.07

= 0.5714