Two groups are competing for the positions of 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

N/a

Explanation

Let `E_(1)=` event of winning of first group,
`E_(2)=` event of winning of second group,
and `E=` event of introducing a new product.
`:.P(E_(1))=0.6., P(E_(2))=0.4`
`P(E//E_(1))=0.7, P(E//E_(2))=0.3`
Now required probability
`P(E_(2)//E)=(P(E_(2)).P(E//E_(2)))/(P(E_(1)).P(E//E_(1))+P(E_(2)).P(E//E_(2)))`
`=(0.4xx0.3)/(0.6xx0.7+0.4xx0.3)=12/54=2/9`