Q. 235.0( 2 Votes )

# 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 was introduced by the second group.

Answer :

Formula: -

Bayes theorem as follows:

Given: -

Let E_{1} be the event of the first group.

P(E_{1}) = 0.6

Let E_{2} be the event of the second group.

P(E_{2}) = 0.4

the Bayes theorem as follows:

Let A be the event when a new product is market.

P (A|E_{1}) = 0.7

P (A|E_{2}) = 0.3

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