A, B, C are three mutually exclusive and exhaustive events associated with a random experiment.

Given : A,B,C are mutually exclusive events and exhaustive events

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

To find : $P(A)$

Formula used: $P(A)+P(B)+P(C)=1$

For mutually exclusive events $A, B$, and $C, P(A$ and $B)=P(B$ and $C)=P(A$ and $C)=0$

Let $P(A)=x, P(B)=(3 / 2) P(A)=\frac{3}{2} x, P(C)=(1 / 2) P(B)=\frac{\frac{1}{2}}{2} \times \frac{3}{2} x=\frac{3}{4} x$

$x+\frac{3}{2} x+\frac{3}{4} x=1$

$\frac{13}{4} x=1$

$x=\frac{4}{13}$

$P(A)=x=\frac{4}{13}$

$P(A)=\frac{4}{13}$