A, B, and C are three mutually exclusive and exhaustive events associated with a random experiment. If P(B) = \(\rm \frac{3}{2}P(A)\) and P(C) = \(\rm \frac{1}{2}P(B)\) then value of P(A) is:
Since A, B, C are mutually exclusive and exhaustive, \(P(A)+P(B)+P(C)=1\).
Step 1 — Express in terms of P(A):
\[P(B)=\tfrac{3}{2}P(A),\quad P(C)=\tfrac{1}{2}P(B)=\tfrac{3}{4}P(A)\]
Step 2 — Substitute and solve:
\[P(A)+\tfrac{3}{2}P(A)+\tfrac{3}{4}P(A)=1 \implies \tfrac{13}{4}P(A)=1\]
Therefore \(P(A)=\dfrac{4}{13}\).
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