InterviewSolution
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InterviewSolution
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Three persons A, B and C apply for a job of manager in a private company. Chances of their selection are in the ratio 1 : 2 : 4. The probability that A, B and C can introduce changes to increase the profits of a company are 0.8, 0.5 and 0.3 respectively. If increase in the profit does not take place, find the probability that it is due to the appointment of A. |
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Answer» \(P(A) = \frac1 {1 + 2 + 4} = \frac17\) \(P(B) = \frac27 \) \(P(C)=\frac{4}{7}\) Let E be the event of increasing in profit. \(\therefore P\left(\frac EA\right) = 0.8\) \(P\left(\frac EB\right) = 0.5\) \(P\left(\frac EC\right) = 0.3\) \(\therefore P\left(\frac{E'}{A}\right)= 1- 0.8 = 0.2\) \(P\left(\frac{E'}{B}\right)= 1- 0.5 = 0.5\) \(P\left(\frac{E'}{C}\right)= 1- 0.3 = 0.7\) \(P\left(\frac A{E'}\right)= \frac{P\left(\frac{E'}A\right) P(A)}{P\left(\frac{E'}A\right)P(A) + P\left(\frac{E'}{B}\right) P(B) + P\left(\frac{E'}{C}\right)P(C)}\) \(= \cfrac{0.2 \times \frac17}{0.2 \times \frac17 + 0.5 \times \frac27 + 0.7 \times \frac47}\) \(= \frac{0.2}{0.2 + 1 + 2.8}\) \(= \frac{0.2}{4}\) \(= \frac2{40}\) \(= \frac1{20}\) \(= 0.05\) Hence, the probability that if increases in profit does not take place, then it is due to the appointment of \(A = P\left(\frac A{E_1}\right) = 0.05\) |
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