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Question: Let A and B are event’s of an experiment and P(1) =\(\frac { 1 } { 4 }\), P(AÈB) =\(\frac { 1 } { 2...

Let A and B are event’s of an experiment and P(1) =14\frac { 1 } { 4 },

P(AÈB) =12\frac { 1 } { 2 }, then value of P is

A

23\frac { 2 } { 3 }

B

13\frac { 1 } { 3 }

C

56\frac { 5 } { 6 }

D

12\frac { 1 } { 2 }

Answer

13\frac { 1 } { 3 }

Explanation

Solution

P(1) = 12\frac { 1 } { 2 }

P=

[Q P(A È B) + P(2) – P(A Ç B)]

= 12−141−14=14⋅43=13\frac { \frac { 1 } { 2 } - \frac { 1 } { 4 } } { 1 - \frac { 1 } { 4 } } = \frac { 1 } { 4 } \cdot \frac { 4 } { 3 } = \frac { 1 } { 3 }