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If 0 lt P(A) lt 1, 0 lt P(B) lt 1 and P...

If ` 0 lt P(A) lt 1, 0 lt P(B) lt 1` and `P(A cup B)=P(A)+P(B)-P(A)P(B)`, then

A

`P(B//A)=P(B)-P(A)`

B

`P(A'-B')=P(A')-P(B')`

C

`P(a cup B)'=P(A)'P(B)'`

D

`P(A//B)=P(A)-P(B)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `P(A nn B)=P(A).P(B)`
It means A and B are independent events, so A' and B' are also independent.
`:. P(A uu B)'=P(A' nn B')=P(A)'.P(B)'`
Alternative Solution
`P(AuuB)'=1-P(AuuB)=1-{P(A)+P(B)-P(A).P(B)}`
`={1-P(A)}{1-P(B)=P(A)'P(B)'`
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