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Question: If A and B are two events such that \(P ( A ) = \frac { 1 } { 3 }\), \(P ( B ) = \frac { 1 } { 4 }\)...

If A and B are two events such that P(A)=13P ( A ) = \frac { 1 } { 3 }, P(B)=14P ( B ) = \frac { 1 } { 4 } and P(A∩B)=15P ( A \cap B ) = \frac { 1 } { 5 } then P(BˉAˉ)=P \left( \frac { \bar { B } } { \bar { A } } \right) =

A

3740\frac { 37 } { 40 }

B

3745\frac { 37 } { 45 }

C

2340\frac { 23 } { 40 }

D

None of these

Answer

3740\frac { 37 } { 40 }

Explanation

Solution

P(BˉAˉ)=1−P(A∪B)P(Aˉ)=1−23601−13=3760×32=3740P \left( \frac { \bar { B } } { \bar { A } } \right) = \frac { 1 - P ( A \cup B ) } { P ( \bar { A } ) } = \frac { 1 - \frac { 23 } { 60 } } { 1 - \frac { 1 } { 3 } } = \frac { 37 } { 60 } \times \frac { 3 } { 2 } = \frac { 37 } { 40 }