Let 0 < P(A) < 1, 0 < P(B) <

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

Let 0 < P(A) < 1, 0 < P(B) < 1 and P(A ∪ B) = P(A) + P(B) - P(A)P(B). Then:

Options:

P(B/A) = P(B) - P(A)

P(A^c ∪ B^c) = P(A^c) + P(B^c)

P(A ∪ B)^c = P(A^c) + P(B^c)

P(A/B) = P(A)

Correct Answer:

P(A/B) = P(A)

Explanation:

P(A ∪ B) = P(A) + P(B) - P(A).P(B)

⇒ P(A ∩ B) = P(A).P(B)

$⇒P(A/B)=\frac{P(A ∩ B)}{P(B)}= P(A)$