Let the events be described as below :

A : No change takes place

E_{1} : Person A gets appointed

E_{2} : Person B gets appointed

E_{3} : 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.