Question

If A and B are two mutually exclusive and exhaustive events with $P\left(B\right)=3P\left(A\right),$ then what is the value of $P\left(\overline{B}\right)$?

• A. $\frac{3}{4}$
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{1}{4}$

Since P(A) and P(B) are two mutually exclusive and exhaustive events, $P\left(A\right)+P\left(B\right)=1$ and $P\left(B\right)=3P\left(A\right)$

$\Rightarrow P\left(A\right)+3P\left(A\right)=1$

$\Rightarrow 4P\left(A\right)=1$

$\Rightarrow P\left(A\right)=\frac{1}{4}$

$\Rightarrow P\left(B\right)=1-\frac{1}{4}=\frac{3}{4}$

$\Rightarrow$ $P\left(\overline{B}\right)$ $=1-\frac{3}{4}=\frac{1}{4}$.