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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 98
Total: 101
Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
Solution:  
E1 : Red ball is transferred from Bag I to Bag II
E2 : Black ball is transferred from Bag I to Bag II
and A :Red ball is drawn from Bag II.
∴P(E1)=
3
7
,P(E2)=
4
7

Also P(A|E1)=
5
10
=
1
2
 and P(A|E2)=
4
10
=
2
5
P(E2|A)=
P(E2).P(A|E2)
P(E1).P(A|E1)+P(E2).P(A|E2)
=
4
7
×
2
5
3
7
×
1
2
+
4
7
×
2
5
=
16
31
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