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 and C occur) is equal to

Step-by-step solution

Given, P(A)=P(B)=P(C)=PP (At least two of A, B, C occur) = (P B C^ )+P (A B^ C )+P (A^ B C )+P(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(A) P(B)[1-P(C)]+P(A)[1-(B)] P(C)+[1-P(A)] P(B) P(C)+P(A) P(B) P(C)=P P (1-P)+(1-P) P P+P (1-P) P+P P P=P²[(1-P)+(1-P)+(1-P)+P]=P²[3-2 P]=3 P²-2 P³P ( . At least two of A, B, C occur) is 3 P²-2 P³ .