Q. 163.7( 3 Votes )

If A, B and C are independent events such that P(A) = P(B) = P(C) = p, then find the probability of occurrence of at least two of A, B and C.

Answer :

Given, P(A)=P(B)=P(C)=p

P(occurrence of at least two of A,B,C)=P(A)P(B)P(C ̅ )+P(A)P(B ̅ )P(C)+P(A ̅ )P(B)P(C)+P(A)P(B)P(C)


=p×p(1-p)+p×(1-p)p+(1-p)p × p + p × p × p


=3p2 (1-p)+p3


=3p2 -3p3 +p3


=3p2 -2p3


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