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 1

Let E_1: 'First group wins' and E₂: 'Second group wins'

⇒  `P (E_1) = 0.6 = 6/10`

and `P (E_2) = 0.4 = 4/10`

Let A: 'New product is introduced`

Then `P (A|E_1) = 0.7 = 7/10`

and `P (A|E_2) = 0.3 = 3/10`

Hence the required probability is

`= P (E_2 |A) = (P(A|E_2) P (E_2))/(P (A|E_1) P (E_1) + P (A| E_2) P (E_2))`

`= (3/10 xx 4/10)/(7/10 xx 6/10 + 3/10 xx 4/10)`

`= 12/(42 + 12)`

`= 12/54`

`= 2/9`