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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 44
Total: 101
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.
Solution:  
Let E1 : ‘First group wins’ and E2 : ‘Second group wins’,
⇒P(E1)=0.6=
6
10
 and P(E2)=0.4=
4
10

Let A : ‘New product is introduced’
Then P(A|E1)=0.7=
7
10
 and P(A|E2)=0.3=
3
10

Hence, the required probability is
=P(E2|A)=
P(A|E2)P(E2)
P(A|E1)P(E1)+P(A|E2)P(E2)
=
3
10
×
4
10
7
10
×
6
10
+
3
10
×
4
10
=
2
9
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