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Question

# Assertion : Two events A and B are such that P(A)=13 and P(B)=23 then P(A∪B)≥23 Reason : If P(B)>P(A), then P(A∪B)≥P(B)

A
Both assertion and reason are true and reason is the correct explanation of assertion.
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B
Both assertion and reason are true but reason is not the correct explanation of assertion.
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C
Assertion is true but reason is false.
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D
Assertion is false but reason is true.
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Solution

## The correct option is A Both assertion and reason are true and reason is the correct explanation of assertion.We know that, P(B) = P(A), then, P(B)≤P(A∪B)≤1 and 0≤P(A∩B)≤P(A) Now P(B)=23,P(A)=13 ∴P(B)>P(A)⇒P(A∪B)≥P(B) ⇒P(A∪B)≥23 So, assertion and reason both are true and reason is the correct explanation of assertion.

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