Let A, B and C be three events associated with sample spaces S . A, B and C are pair wise independent and P(A)=P(B)=P(C)=P . If all of them cannot occur simultaneously, then P(A B C) is equal to

Step-by-step solution

A, B, C are pair-wise independent events. aligned & P(A B)=P(A) P(B) & P(B C)=P(B) P(C) & P(C A)=P(C) P(A) aligned and P(A)=P(B)=P(C)=P and P(A B C)=0 [ they cannot occur simultaneously] Now, P(A B C)=P(A)+P(B)+P(C)-P(A B)-P(B C)-P(C A)+P(A B C)=P+P+P-P(A) P(B)-P(B) P(C)-P(C) P(A)+0=3 P-P P-P P-P P=3 P-P^2-P^2-P^2=3 P-3 P^2=3 P(1-P)