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Question: If \(P ( B ) = \frac { 3 } { 4 } , P ( A \cap B \cap \bar { C } ) = \frac { 1 } { 3 }\) and \(P ( \b...

If P(B)=34,P(A∩B∩Cˉ)=13P ( B ) = \frac { 3 } { 4 } , P ( A \cap B \cap \bar { C } ) = \frac { 1 } { 3 } and P(Aˉ∩B∩Cˉ)=13P ( \bar { A } \cap B \cap \bar { C } ) = \frac { 1 } { 3 }, then

P(B∩C)P ( B \cap C ) is

A

1/12

B

1/6

C

1/15

D

1/9

Answer

1/12

Explanation

Solution

From Venn diagram, we can see that

P(B∩C)=P(B)−P(A∩B∩Cˉ)−P(Aˉ∩B∩Cˉ)P ( B \cap C ) = P ( B ) - P ( A \cap B \cap \bar { C } ) - P ( \bar { A } \cap B \cap \bar { C } )

=34−13−13=112= \frac { 3 } { 4 } - \frac { 1 } { 3 } - \frac { 1 } { 3 } = \frac { 1 } { 12 }

.