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Three persons A, B and C apply for a job of Manager in a Private company. Chance of their selection (A, B and C) are in the ratio 1 : 2 : 4. The probability that. A, B and C can introduce changes to improve profits of company are 0.8, 0.5 and 0.3 respectively, if the changes does not take place, find the probability that it is due to the appointment of C.

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Let the events be described as below :

A : No change takes place

E1 : Person A gets appointed

E2 : Person B gets appointed

E3 : Person C gets appointed

The chances of selection of A, B and C are in the ratio 1 :2: 4.

Hence,

Probabilities of A, B and C introducing changes to improve profits of company are 0.8, 0.5 and 0.3 respectively. 

Hence probability of no changes on appointment of A, B and C are  0.2, 0.5 and 0.7 respectively.

Hence,

.'.   If no change takes place, the probability that it is  due to appointment of C is 7/10.

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