Q. 224.0( 2 Votes )

# Two groups are competing for the positions of the Board of Directors of corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.

Answer :

Let us assume U_{1}, U2 and A be the events as follows:

U_{1} = First team wins

U_{2} = Second team wins

A = Introduction of project

From the problem ir is given that,

⇒

⇒

⇒ P(A|U_{1}) = P(introduction of project by team 1) = 0.7

⇒ P(A|U_{2}) = P(introduction of project by team 2) = 0.3

Now we find

P(U_{2}|A) = P(Project introduced by team 2)

Using Baye’s theorem:

⇒

⇒

⇒

⇒

⇒

∴ The required probability is .

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