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Question

If A and B are two events such that P(A)=12, and P(B)=23, then


A

P(AUB)2/3

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B

16≤P(A∩B)≤1/2

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C

16P(A'∩B)≤1/2

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D

All of these

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Solution

The correct option is D

All of these


Step 1. Find the value of P(AUB)

Given data,

PA = 12

PB = 23

We know that, P(AUB) max P(A),P(B) = 23

Step 2. Find the value of P(A∩B)

We know that, P(A∩B) min P(A),P(B) =12

As P(A∩B) = P(A)+P(B)-P(A∪B)

PA+PB-1

12 + 23 -1

16

Therefore, 16P(A∩B)12

Step 3. Find the value of P(A'∩B)

We know that, P(A'∩B)=P(B)-P(A∩B)

So, 23-12 P(A'∩B) 23-16

16 P(A'∩B)12

Hence, all the given statements are true.

Therefore, option "D" is correct.


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