Question

Two groups are competing for the position on the board 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 correspondind probability if 0.3,if the second group wins.Find the probability that the new product introduced was by the second group.

Answer 1

The correct answer is: $\frac{2}{9}$
Given;
Probability that the first group wins the competition=$P(G_1)=0.6$
Probability that the second group wins the competition=$P(G_2)=0.4$
Let $P$ denotes the lauching of new product.
$∴(P|G_1)=0.7,(P|G_2)=0.3$
By using Bayes’ theorem, we obtain;
$P(G_1|P)=\frac{P(G_2)P(P|G_2)}{P(G_1)P(P|G_1)+P(G_2)P(P|G_2)}$
$=\frac{0.4×0.3}{0.6×0.7+0.4×0.3}$
$=\frac{12}{54}$
$=\frac{2}{9}$