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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 27
Total: 101
Events A and B are such that P(A)=
1
2
, P(B)=
7
12
 and P(not A or not B) =
1
4
. State whether A and B are independent ?
Solution:  
Given that P (not A or not B) =
1
4

⇒P(Ac∪Bc)=
1
4

⇒P((A∩B)c)=
1
4

⇒1−P(A∩B)=
1
4

⇒P(A∩B)=1−
1
4
=
3
4

Also, P(A)×P(B) =
1
2
×
7
12
=
7
24
≠
3
4

⇒P(A)×P(B)≠P(A∩B)
∴ A and B are not independent.
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