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Question

For two events Aand B,if P(A)=P(A/B)=14 and P(B/A)=12, then


A

Aand B are independent

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B

P(A'/B)=34

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C

P(B'/A')=12

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D

All of the above

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Solution

The correct option is D

All of the above


The explanation for the correct options:

Step1. Check A and B are independent:

We know that

PBA=P(BA)P(A)=12

P(BA)=18

PAB=P(AB)P(B)=14

P(B)=12

P(AB)=P(A).P(B)=14×12=18

So, A and Bare independent.

Step2. Find the value ofPA'B:

Now,PA'B=P(A'B)P(B)=P(A')P(B)P(B)

=34×1212

PA'B=34

Step3. Find the value ofPB'A':

Now,PB'A'=P(B'A')P(A')

=[P(B').P(A')]P(A')=12

Hence, Option (D) is the correct answer.


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