If A and B are any two events such that P(AUB) = P(A) then

Question

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If A and B are any two events such that P(AUB) = P(A) then

Answer 1

Correct option is (b) \(P (\frac AB) = 1\)

\(P(A \cup B) = P(A)\)

⇒ \(P(A) + P(B) - P(A \cap B) = P(A)\)

⇒ \(P(B) = P(A \cap B)\)

\(P (\frac BA) = \frac{P(B\cap A)}{P(A)} = \frac{P(B)}{P(A)} < 1 \ne 1\)

\(P (\frac AB) = \frac{P(A\cap B)}{P(B)} = \frac{P(B)}{P(B)} =1\)