One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?

$E:$ 'the card drawn is a spade'

$F:$ 'the card drawn is an ace'

In a deck of $52$ cards, $13$ cards are spades and $4$ cards are aces.

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

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

In the deck of cards, only $1$ card is an ace of spades.

$ \mathrm{P}(\mathrm{EF})=\mathrm{P}$ (the card drawn is spade and an ace) $=\frac {1}{52}$

$\mathrm{P}(\mathrm{E}) \times \mathrm{P}(\mathrm{F})=\frac{1}{4} \frac{1}{13}=\frac{1}{52}=\mathrm{P}(\mathrm{EF})$

$\Rightarrow \mathrm{P}(\mathrm{E}) \times \mathrm{P}(\mathrm{F})=\mathrm{P}(\mathrm{EF})$

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