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If A and B are two events such that P(A/...

If `A` and `B` are two events such that `P(A//B)=p ,` `P(A)=p ,` `P(B)=1/3` and `P(AuuB)=5/9` then `p=`

A

a) `2/3`

B

b) `3/5`

C

c) `1/3`

D

d) `3/4`

Text Solution

Verified by Experts

The correct Answer is:
c) `1/3`
Given, `P(A//B)=p ,` `P(A)=p ,` `P(B)=1/3` and `P(AuuB)=5/9`

`P(A//B)=(P(AnnB))/(P(B))=p`

`P(AnnB)=p/3`


We know,

`P(AuuB)=P(A)+P(B)-P(AnnB)`

`5/9=p+1/3-p/3`

...
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