Question

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

If $P\left(B\right)=\left(\frac{3}{2}\right)P\left(A\right)$ and $P\left(C\right)=\left(\frac{1}{2}\right)P\left(B\right),$ find P(A).

Answer 1

A, B, C being mutually exclusive exhaustive events, we have
$P\left(A\right)+P\left(B\right)+P\left(C\right)=1$

$\Rightarrow$ P(A) + $\frac{3}{2}$ P(A) + $\frac{1}{2}$. $\frac{3}{2}$ P(A) = 1
$\Rightarrow$ $\frac{13}{4}$ P(A) = 1

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