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If P(B)=3/4, P(AnnBnnbarC)=1/3 and P(bar...

If `P(B)=3/4, P(AnnBnnbarC)=1/3` and `P(barAnnBbarC)=1/3` then `P(BnnC)=`

A

`(1)/(12)`

B

`(1)/(6)`

C

`(1)/(15)`

D

`(1)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
`P{(bar(A)nn(B nn bar(C ))}=P(B nn bar(C ))-P(A nn B nn bar(C ))`
`= P(B)-P(B nn C)-P(A nn B nn bar(C ))`
`rArr -P(bar(A)nn B nn bar(C ))-P(A nn B nn bar(C ))+P(B)=P(B nnC)`
`rArr " " P(B nn C)=(3)/(4)-(1)/(3)-(1)/(3)=(1)/(12)`
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