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Let Xa n dY be two events that P(X)=1/3,...

Let `Xa n dY` be two events that `P(X)=1/3, P(X"|"Y)=1/2a n dP(Y"|"X)=2/5` then:

A

`P(Y)=(4)/(5)`

B

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

C

`P(XcupY)=(2)/(5)`

D

`P(XcapY)=(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
P(X) = `(1)/(3)`
`P((X)/(Y)) = P(X nn Y)/(P(Y)) = (1)/(2)`
`P((X)/(Y)) = (P(X nn Y))/(P(X)) = (2)/(5)`
`P(X nn Y) = (2)/(5)`
`P(Y) = (4)/(15)`
`P((X')/(Y)) = (P(Y) - P(X nn Y))/(P(Y)) = ((4)/(15) - (2)/(15))/((4)/(15)) = (1)/(2)`
`P(X nn Y) = (1)/(3) + (4) /(15) - (2)/(15) = (7)/(15) = (7)/(15)`
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Knowledge Check

  • Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2and P(Y|X)=2/5. Then

    A
    `P(Y)=4/15`
    B
    `P(X'|Y)=1/2`
    C
    `P(XuuY)=2/5`
    D
    `P(XnnY)=1/5`

  • Let X and Y be two events such that P(X|Y)=(1)/(2),P(Y|X)=1/3 and P(X capY)=(1)/(6) , which of the following is correct ?

    A
    `P(XcupY)=2/3`
    B
    X and Y are independent
    C
    X and Y are not independent
    D
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  • If X and Y are two events such that PX//Y)=(1)/(2), P(Y//X)=(1)/(3) and P(XcapY)(1)/(6) . Then, which of the following is/are correct ?

    A
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    C
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    D
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