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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)=0.3`, `P(B)=0.25`, `P(AnnB)=0.2`, then `P(((A^(C ))/(B^(C )))^(C ))` is equal to

A

`(2)/(15)`

B

`(11)/(15)`

C

`(13)/(15)`

D

`(14)/(15)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `P(((A^(C ))/(B^(C )))^(C ))=1-P((A^(C ))/(B^(C )))`
`=1-(P(A^(C )nnB^(C )))/(P(B^(C )))`
`=1-(1-P(AuuB))/(1-P(B))`
`=1-(1-P(A)-P(B)+P(AnnB))/(1-P(B))`
`=1-(0.65)/(0.75)=1-(13)/(15)=(2)/(15)`
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