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If A and B are exhaustive events in a sa...

If `A` and `B` are exhaustive events in a sample space such that probabilites of the events `AnnB`, `A`, `B` and `AuuB` are in `A.P.` If `P(A)=K`, where `0 lt K le 1`, then

A

`P(B)=(K+1)/(2)`

B

`P(AnnB)=(3K-1)/(2)`

C

`P(AuuB)=1`

D

`P(A'uuB')=(3(1-K))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`(a,b,c,d)` `A`, `B` are exhaustive events `implies AuuB=S`
`impliesP(AuuB)=1`
`2P(B)=P(A)+P(AuuB)=K+1`
`impliesP(B)=(K+1)/(2)-P(AuuB)-P(A)-P(B)`
`=-1K-((K+1))/(2)=(2-2K-K-1)/(2)`
`:. P(AnnB)=(3K-1)/(2)`
`P(A'uuB')=P((AnnB)')`
`=1-P(AnnB)`
`=1-(3K-1)/(2)`
`=(3(1-K))/(2)`
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