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If events are independents and P(A)=(1)/...

If events are independents and `P(A)=(1)/(3), P(B)=(1)/(3)` and `P(C )=(1)/(4)`, then `P(A' nn B' nn C')` is equal to

A

`(1)/(4)`

B

`(1)/(12)`

C

`(1)/(3)`

D

`(5)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `P(A)=(1)/(3), P(B)=(1)/(3)` and `P(C )=(1)/(4)`
`therefore P(A')=(2)/(3), P(B')=(2)/(3)`
and `P(C')=(3)/(4)`
Now, `P(A'nn B'nn C')=P(a')P(B')P(C')`
[since, A,B and C are independent events]
`=(2)/(3)xx(2)/(3)xx(3)/(4)=(1)/(3)`
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