Question

Given that $E$ and $F$ are events such that $P\left(E\right)=0.6,P\left(F\right)=0.3$ and $P(E\cap F)=0.2$, then the value of $P\left(E/F\right)$ and $P\left(F/E\right)$ is:

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

Answer 1

The correct option is A $\frac{2}{3},\frac{1}{3}$

Given $P\left(E\right)=0.6,P\left(F\right)=0.3$ and $P(E\cap F)=0.2$
We know that by the definition of conditional probability,
$P\left(E/F\right)=\frac{P(E\cap F)}{P\left(F\right)}$
By substituting the values we get
$\Rightarrow P\left(E/F\right)=\frac{P(E\cap F)}{P\left(F\right)}=\frac{0.2}{0.3}=\frac{2}{3}$
$\Rightarrow P\left(F/E\right)=\frac{P(E\cap F)}{P\left(E\right)}=\frac{0.2}{0.6}=\frac{2}{6}=\frac{1}{3}$