In a deck of $52$ cards, $4$ cards are kings, $4$ cards are queens, and $4$ cards are jacks.

$\therefore \mathrm{P}(\mathrm{E})=\mathrm{P}$ (The card drawn is a king or a queen) $=\frac{8}{52}=\frac{2}{13}$

$\therefore \mathrm{P}(\mathrm{F})=\mathrm{P}$ (The card drawn is a king or a jack) $ =\frac{8}{52}=\frac{2}{13}$

There are $4$ cards which are king and queen or jack.

$\therefore $ $\mathrm{P}(\mathrm{EF})=\mathrm{P}$ (The card drawn is king or a queen, or queen or a jack) $=\frac{4}{52}=\frac{1}{13}$.

$\mathrm{P}(\mathrm{E}) \times \mathrm{P}(\mathrm{F})=\frac{2}{13} \cdot \frac{2}{13}=\frac{4}{169} \neq \frac{1}{13}$

$\Rightarrow \mathrm{P}(\mathrm{E}), \mathrm{P}(\mathrm{F}) \neq \mathrm{P}(\mathrm{EF})$

Therefore, the given events $E$ and $F$ are not independent.