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Question

Consider two events A and B such that P(A)=14, P(BA)=12, P(AB)=14. For each of the following statements, which is true.

I.P(A'B')=34

II. The events A and B are mutually exclusive

III.P(AB)+P(AB')=1


A

Ionly

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B

I&II

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C

I&III

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D

II&III

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Solution

The correct option is A

Ionly


Explanation for correct option.

Given,

A&Bare two event such that P(A)=14,P(BA)=12, P(AB)=14.

Step1. explanation for statement I

I.P(A'B')=34

Given, P(AB)=14

Therefore,

P(A'B')=1-P(AB)=1-14=34

Statement I is true.


Step2. Explanation for statement II

II. The events A and B are mutually exclusive.

P(BA)=P(AB)P(A)12=P(AB)14P(AB)=18

Therefore ‘A’ & ‘B’ are not mutually exclusive events.

Step3. Explanation for Statement III.

P(AB)+P(AB')=14+[P(A)-P(AB)P(B')]=14+14-1812=14+14=14

But, P(AB)+P(AB')=1

Statement III is also wrong.

Hence, the correct option is (A).


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