State True or False for the statements in the Exercise.

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

True

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.