Question

A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = (3/2) P(A) and P(C) = (1/2) P(B), find P(A).

Answer 1

Here, P(A) + P(B) + P(C) = 1 …(1)

For mutually exclusive events A, B, and C,

P(A and B) = P(B and C) = P(A and C) = 0

Given: P(B) = (3/2) P(A) and P(C) = (1/2) P(B)

(1) => P(A) + (3/2) P(A) + (1/2) P(B) = 1

=> P(A) + (3/2) P(A) + (1/2){(3/2) P(A)} = 1

=> P(A) + (3/2) P(A) + (3/4) P(A) = 1

=> 13/4 P(A) = 1

or P(A) = 4/13