If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B)= 3 2 P(A) and P(C)= 1 2 P(B) , then P(A C) equals to

Step-by-step solution

Given, P(B)= 3 2 P(A) and P(C)= 1 2 P(B) Since, A, B and C are exclusive events. aligned & & P(A)+P(B)+P(C) & =1 & & P(A)+ 3 2 P(A)+ 1 2 3 2 P(A) & =1 & & P(A) (1+ 3 2 + 3 4 ) & =1 & & 13 4 P(A) & =1 & & P(A) & = 4 13 & & P(C)= 1 2 3 2 P(A) & = 3 4 4 13 = 3 13 aligned Also, A, B and C are mutually exclusive. aligned & P(A B)=P(B C)=P(C A)=0 & P(A C)=P(A)+P(B)-0 & = 4 13 + 3 13 = 7 13 aligned