In a deck of $52$ cards, $26$ cards are black and $4$ cards are kings.

$\therefore $ $\mathrm{P}(\mathrm{E})=\mathrm{P}$ (the card drawn is a black ) $=\frac{26}{52}=\frac{1}{2}$

$\therefore $ $\mathrm{P}(\mathrm{F})=\mathrm{P}$ (the card drawn is a king ) $=\frac{4}{52}=\frac{1}{13}$

In the pack of $52$ cards, $2$ cards are black as well as kings.

$\therefore $ $\mathrm{P}(\mathrm{EF})=\mathrm{P}$ (the card drawn is  black king ) $=\frac{2}{52}=\frac{1}{26}$

$\mathrm{P}(\mathrm{E}) \times \mathrm{P}(\mathrm{F})=\frac{1}{2} \cdot \frac{1}{13}=\frac{1}{26}=\mathrm{P}(\mathrm{EF})$

Therefore, the given events $\mathrm{E}$ and $\mathrm{F}$ are independent.