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Q. 9   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 are0.6 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.

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A: the first groups will win

B:  the second groups will win

P(A)=0.6

P(B)=0.4

X: Event of introducing a new product.

Probability of introducing a new product if the first group wins : P(X|A)=0.7

Probability of introducing a new product if the second group wins : P(X|B)=0.3

P(B|X)= \frac{P(B).P(X|B)}{P(B).P(X|B)+P(A).P(X|A)}

p(B|X) = \frac{0.4\times 0.3}{0.4\times 0.3+0.6\times 0.7}

p(B|X) = \frac{0.12}{0.12+0.42}

p(B|X) = \frac{0.12}{0.54}

p(B|X) = \frac{12}{54}

p(B|X) = \frac{2}{9}

Hence,  the probability that the new product introduced was by the second group : 

                                                                                                                                  p(B|X) = \frac{2}{9} 

 

Posted by

seema garhwal

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