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NDA Math Probability Part 2
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© examsnet.com
Question : 57
Total: 59
Two independent events A and B are such that P( A ∪ B)=
2
3
and P( A∩ B)=
1
6
. If P|B|< P( A) , then what is P(B) equal to?
[NDA I 2019]
1
4
1
3
1
2
1
6
Validate
Solution:
(B)
Since A and B are independent events P( A∩ B) = P( A). P(B)
⇒ P( A) .P(B) =
1
6
….(i)
Now P( A ∪ B) =
2
3
⇒ P( A) + P(B) − P( A∩ B) =
2
3
⇒ P( A) + P(B) −
1
6
=
2
3
⇒ P( A)+P(B) =
5
6
…(ii)
From (i) and (ii)
P(B) =
1
3
,
1
2
⇒ P(B) = 1/3 ( given P(B) < P( B) < P(A) )
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