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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 26
Total: 101
If A and B are two events such that P(A)=
1
4
, P(B)=
1
4
 P(A∩B)=
1
8
 , find P (not A and not B).
Solution:  
As P(A∩B)=
1
8
=
1
4
×
1
2
 =P(A)×P(B),
⇒ A and B are independent.
⇒ Ac and Bc are also independent.
⇒P(Ac∩Bc)=P(Ac)P(Bc)
⇒P(Ac∩Bc)=(1−P(A))(1−P(B))
=(1−
1
4
)(1−
1
2
) =
3
4
×
1
2
=
3
8
. (∵P(Ac)=1−P(A)&P(Bc)=1−P(B))
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