12) If P(B) =1/3,n(S)=24,then what is n(B)
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0
Answer:
Answer
Correct option is
C
42
25
Here, P(A)=
5
2
, P(B)=
10
3
and P(A ∩ B) =
5
1
P(A
′
∣B
′
)=
P(B)
P(A
′
capB
′
)
=
1−P(B)
1−P(A∪B)
=
1−P(B)
1−[P(A)+P(B)−P(A∩B)]
=
1−
10
3
1−(
5
2
+
10
3
−
5
1
)
=
10
7
1−(
10
4+3−2
)
=
10
7
1−
2
1
=
7
5
P(B
′
∣A
′
)=
P(A
′
)
P(B
′
∩A
′
)
=
1−P(A)
1−P(A∪B)
=
1−
5
2
1−
2
1
=
3/5
1/2
=
6
5
[∵P(A∪B)=
2
1
]
∴P(A
′
∣B
′
)⋅P(B
′
∣A
′
)=
7
5
−
6
5
=
42
25
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