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If A and B are two Mutually Exclusive ev...

If `A and B` are two Mutually Exclusive events in a sample space `S` such that `P(B) = 2 P(A)` and `A uu B=S`, then `P(A)=`

A

`(2)/(3)`

B

`(1)/(3)`

C

`(1)/(4)`

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `A uu B = S`
`therefore P(A uu B)= P(S)=1`
`rArr P(A)+P(B)=1 " " [because P(A nn B)=0]`
`rArr P(A)+2P(A)=1`
`therefore " " P(A)=(1)/(3) " " [because P(B) = 2P(A), "given"]`
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