CBSE Class 12 Math 2009 Solved Paper

Question : 23 of 29

Marks: +1, -0

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

E_1

be the event of the first group winning and

E_2

be the event of the second group winning and S be the event of introducing a new product.
P(

E_1

) = 0.6 P(

E_2

) = 0.4
P (S|

E_1

) = 0.7
P (S|

E_2

) = 0.3
Probability of a new product being introduced by the second group will be , P (

E_2

|S)
P (

E_2

|S) =

{P(E_2).P(S|E_2)}/{P(E_1).P(S|E_1)+P(E_2).P(S|E_2)}

{0.4×0.3}/{0.4×0.3+0.7×0.6}

{0.12}/{0.12+0.42}

P (

E_2

|S) =

{12}/{54}

2/9

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