JIPMAT 2023 (QA) - Let A and B be two events such that P(A)=0.25, P(B)=0.50 and P(A ∩ B)=0.14. The probability that neither A nor B occurs is: | PYQs + Solutions | AfterBoards
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JIPMAT 2023

Modern Math
>
Probability

Conceptual

Let A and B be two events such that P(A)=0.25, P(B)=0.50 and P(A ∩ B)=0.14. The probability that neither A nor B occurs is:

Correct Option: 3
Given: \newline P(A)=0.25P(A) = 0.25
P(B)=0.50P(B) = 0.50
P(A∩B)=0.14P(A ∩ B) = 0.14
To find P(neither A nor B) =P(A′∩B′)=1−P(A∪B)= P(A' ∩ B') = 1 - P(A ∪ B)
Using: P(A∪B)=P(A)+P(B)−P(A∩B)P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
=0.25+0.50−0.14= 0.25 + 0.50 - 0.14
=0.61= 0.61
Therefore, P(neither A nor B) =1−0.61=0.39= 1 - 0.61 = 0.39

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