Question

If A, B and C are three mutually exclusive and exhaustive events. Find P(A), if P(B) = $\frac{3}{2}$ P(A) and P(C) = $\frac{1}{2}P\left(B\right)$.

• A. $\frac{8}{13}$
• B. $\frac{5}{13}$
• C. $\frac{4}{13}$
• D. $\frac{9}{13}$

Answer 1

The correct option is C $\frac{4}{13}$

Let P(A) = x, then P(B) $=\frac{3}{2}$ x and P(C) $=\frac{1}{2}\ast \frac{3}{2}\times =\frac{3}{4}x\therefore P\left(A\right)+P\left(B\right)+P\left(C\right)=P(A\cup B\cup C)=P\left(S\right)=1\therefore x+\frac{3}{2}x+\frac{3}{4}x=1\Rightarrow x=\frac{4}{13}\therefore P\left(A\right)=\frac{4}{13}$