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.
Given: let E1 be the event that first group wins the competition, E2 be the event that that second group wins the competition and A be the event of introducing 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 of that new product introduced was by the second group, being given that a new product was introduced, is P(E2|A).
By using bayes’ theorem, we have:
