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If (A) =1/3 ,P(B) =1/2 and P(A cup B) =5...

If `(A) =1/3 ,P(B) =1/2 and P(A cup B) =5/6` then events A and B are

A

mutually exclusive

B

independent as well as mutually exclusive

C

independent

D

dependent only on A

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`P(A)=(2)/(3), P(B)=(1)/(2) " and " P(A cup B)=(5)/(6)`
`therefore P(A cup B)=P(A)+P(B)-P(A cup B)`
`implies P(A cup B)=(2)/(3)+(1)/(2)-(5)/(6)=(1)/(3)`
Clearly, P(AB)=P(A)P(B)
Hence, A and B are independent events.
Since independent events are never mutually exclusive.
So, option (c ) is correct.
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