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).
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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