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).
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 $P(A)=x, P(B)=(3 / 2) P(A)=\frac{3}{2} x, P(C)=(1 / 2) P(B)=\frac{\frac{1}{2}}{2} \times \frac{3}{2} x=\frac{3}{4} x$
$x+\frac{3}{2} x+\frac{3}{4} x=1$
$\frac{13}{4} x=1$
$x=\frac{4}{13}$
$P(A)=x=\frac{4}{13}$
$P(A)=\frac{4}{13}$
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