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Question -

Two groups are competing for the position on the Board of directors of a 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 new 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 E1 bethe event that first group wins the competition, E2 be theevent that that second group wins the competition and A be the event ofintroducing a new product.

Then P (E1)= 0.6 and P (E2) = 0.4

Also P (A|E1)= P (introducing a new product given that first group wins) = 0.7

And P (A|E2)= P (introducing a new product given that second group wins) = 0.3

Now the probability ofthat new product introduced was by the second group, being given that a newproduct was introduced, is P (E2|A).

By using Bayes’theorem, we have

P (E2|A) =2/9

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