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