A bank hires three consulting firm to upgrade the software program. Firm A is us

Question

A bank hires three consulting firm to upgrade the software program. Firm A is used 40% of the time that this type of work is seeded. Firm B and C are used both 30% of the time by the bank. Of the overall time that the bank uses these Firms, 10% of the time of firm A, 8% of Firm A, 8% fo Firm B and 12% of Firm C are used by the bank to upgrade a Microsoft application software program. What is the probability that the bank contracts one of these firms to upgrade a Microsoft software program? 0.14 0.20 0.16 0.22 0.18

Explanation / Answer

From the given information we have

P(A)= 0.40, P(B) = 0.30, P(C)= 0.30

Let S shows the event that tha bank contact the firm for siftware upgrade sp we have

P(S|A) = 0.10, P(S|B) = 0.08, P(S|C) = 0.12

By the law of total probability the requried probability is

P(S) = P(S|A)P(A)+P(S|B)P(B)+P(S|C)P(C) = 0.10 * 0.40 + 0.08*0.30 + 0.12*0.30 = 0.10

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