CBSE Class 12 Math 2009 Solved Paper

Question : 23

Total: 29

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.

Solution:

Let E1 be the event of the first group winning and E2 be the event of the second group winning and S be the event of introducing a new product.
P(E1) = 0.6 P(E2) = 0.4
P (S|E1) = 0.7
P (S|E2) = 0.3
Probability of a new product being introduced by the second group will be , P (E2|S)
P (E2|S) =

P(E2).P(S|E2)

P(E1).P(S|E1)+P(E2).P(S|E2)

0.4×0.3

0.4×0.3+0.7×0.6

0.12

0.12+0.42

P (E2|S) =

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