Question

Let $E$ and $F$ be events with $P\left(E\right)=\frac{3}{5},P\left(F\right)=\frac{3}{10}$ and $P(E\cap F)=\frac{1}{5}$. Are $E$ and $F$ independent ?

• A. True
• B. False

Answer 1

The correct option is B False

It is given that $P\left(E\right)=\frac{3}{5},P\left(F\right)=\frac{3}{10}$ and $P\left(EF\right)=P(E\cap F)=\frac{1}{5}$
$P\left(E\right)\cdot P\left(F\right)=\frac{3}{5}\cdot \frac{3}{10}=\frac{9}{50}\ne \frac{1}{5}$
$\Rightarrow P\left(E\right)\cdot P\left(F\right)\ne P\left(EF\right)$
Therefore, $E$ and $F$ are not independent.