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Let X and Y be two events such that P(X)...

Let X and Y be two events such that `P(X)=1/3, P(X|Y)=1/2and P(Y|X)=1/3.` Then

A

`P(Y)=1/3`

B

`P(X'|Y)=1/2`

C

`P(XuuY)=2/3`

D

`P(XnnY)=1/5`

Text Solution

Verified by Experts

The correct Answer is:
A, B
We have `P(X)=1/3,(P(XnnY))/(P(Y))=1/2and (P(YnnX))/(P(X))=2/5`
`thereforeP(XnnY)=(P(Y))/(2)=2/5P(X)=2/5.""1/3=2/15`
`impliesP(Y)=4/15`
`P(X'//Y)=(P(X'nnY))/(P(Y))`
`=(P(Y)-P(XnnY))/(P(Y))=(4/15-2/15)/(4/15)=2/4=1/2`
`P(XnnY)=P(X)+P(Y)-P(XnnY)`
`=1/3+4/15-2/15=7/15`
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