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 changes do not take place, find the probability that it is due to the appointment of C.
Let us assume U1, U2, U3 and A be the events as follows:
U1 = choosing Person A
U2 = choosing Person B
U3 = choosing Person C
A = Improve in profit occurs
From the problem
⇒ 
⇒ 
⇒ 
⇒ P(A|U1) = P(Change occurs due to person A)
⇒ 
⇒ P(A|U2) = P(Change occurs due to person B)
⇒ 
⇒ P(A|U3) = P(Change occurs due to person C)
⇒ 
Now we find
1 - P(U3|A) = P(The change does not occurred due to appointing C)
Using Baye’s theorem:
⇒ 
⇒ 
⇒
⇒ 
⇒ 
∴ The required probability is 
.