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Question

If two events P(AUB)=56,P(A')=56,P(B)=23then A and B are.


A

Independent

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B

Mutually exclusive

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C

Mutually exhaustive

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D

Dependent

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Solution

The correct option is B

Mutually exclusive


Explanation for the correct answer:

To find the required answer:

Given that P(AUB)=56

P(A')=56, P(B)=23

Then,

P(A)=1-PA'=16

We know, P(AUB)=P(A)+P(B)–P(A∩B)

So,

56=16+23–P(A∩B)⇒56=(1+4)6-P(A∩B)⇒56=56-P(A∩B)⇒P(A∩B)=0

If P(A∩B)=0 then two events are mutually exclusive.

Hence, the correct option is B.


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