If A and B are two events such that P(A∪B) = 3/4 P(A∩B)
Independent
To classify events A and B, we check whether \(P(A \cap B) = P(A) \cdot P(B)\).
Given: \(P(A) = \tfrac{1}{2}\), \(P(B) = \tfrac{1}{3}\), and \(P(A \cap B) = \tfrac{1}{6}\).
Compute the product: \(P(A) \cdot P(B) = \tfrac{1}{2} \times \tfrac{1}{3} = \tfrac{1}{6}\).
Since \(P(A \cap B) = \tfrac{1}{6} = P(A) \cdot P(B)\), the multiplication rule for independent events is satisfied.
Also, \(P(A \cap B) = \tfrac{1}{6} \neq 0\), so A and B are not mutually exclusive.
Hence, A and B are Independent events.
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