For A,B and C the chances of being selected as the manager of a firm are in the ration 4:1:2 respectively. The respective probabilities for them to introduce a radical change in marketing strategy are 0.3, 0.8 and 0.5. If the change does take place, find the probability that it is due to the appointment of B or C.
Let us assume U1, U2, U3 and A be the events as follows:
U1 = choosing Firm A
U2 = choosing Firm B
U3 = choosing Firm C
A = A change takes place
From the problem
⇒ 
⇒ 
⇒ 
⇒ P(A|U1) = P(Change occurs due to firm A)
⇒ 
⇒ P(A|U2) = P(Change occurs due to Firm B)
⇒ 
⇒ P(A|U3) = P(Change occurs due to firm C)
⇒ 
Now we find
P(U2|A) + P(U3|A) = P(The change occurred due to appointing B or C)
Using Baye’s theorem:
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
∴ The required probability is 
.
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