Question

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

Answer 1

$P(E)=\frac{3}{5},$
$P(F)=\frac{3}{10}$
$∴P(E∩F)=\frac{1}{5}$
Now
$P(E).P(F)=\frac{3}{5}×\frac{3}{10}=\frac{9}{50} \neq\frac{1}{5}$
$⇒P(E).P(F)\neq P(EF)$
Therefore, E and F are not independent events.