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Question

Let A and B be two events with P(AC)=0.3,P(B)=0.4 and P(ABC)=0.5. Then, P(B|ABC) is equal to

A
14
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B
13
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C
12
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D
23
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Solution

The correct option is D 14
Given, P(AC)=0.3,P(B)=0.4 and P(ABC)=0.5

P(A)=10.3=0.7,P(B)=10.4=0.6

Now,
P(BABC)=P(B(ABC))P(ABC)

=P(AB)P(A)+P(BC)P(ABC)

=P(A)P(ABC)P(A)+P(BC)P(ABC)

=0.70.50.7+0.60.5=0.20.8=14

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