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

Explanation

To solve the problem step by step, we will use the information given about the selection probabilities and the probabilities of introducing changes. We will also apply Bayes' theorem to find the required probability.

### Step 1: Define Events
Let:
- \( E_1 \): Event that A is selected.
- \( E_2 \): Event that B is selected.
- \( E_3 \): Event that C is selected.
- \( A \): Event that changes take place.
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