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If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P (At least two of A, B, C occur) = 3p^2 – 2p^3

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State True or False for the statements: If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P (At least two of A, B, C occur) = 3p2 – 2p3 Select the correct answer from above options

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Let A, B,C denotes occurrence of events A,B and C and A’,B’ and C’ not occurrence. As, P(A) = P(B) = P(C) = p And P(A’) = P(B’) = P(C’) = p P (At least two of A, B, C occur) = P(A ∩ B ∩ C’) + P(A ∩ B’ ∩ C) + P(A’ ∩ B ∩ C) ∵ events are independent: P (At least two of A, B, C occur) = P(A)P(B)P(C’) + P(A)P(B’)P(C)+P(A’)P(B)P(C) = 3p2(1-p) = 3p2 – p3 Hence, statement is true.

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