From a pack of 52 playing cards, a card is drawn at random. What is the probability that the card is a spade or an ace?

Let's solve this using probability rules for the union of two events:
$$\text{P}(S\cup A)=\text{P}(S)+\text{P}(A)-\text{P}(S\cap A)$$
Where:$S$ is the event of drawing a Spade. A standard deck contains $13$ spades:
$$\text{P}(S)=\frac{13}{52}$$
$A$ is the event of drawing an Ace. A standard deck contains $4$ aces:
$$\text{P}(A)=\frac{4}{52}$$
$S\cap A$ is the event of drawing a card that is both a spade and an ace (the Ace of Spades). There is exactly $1$ such card:
$$\text{P}(S\cap A)=\frac{1}{52}$$
Substitute these values into the formula:
$$\text{P}(S\cup A)=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{13+4-1}{52}=\frac{16}{52}$$
Simplifying the fraction by dividing the numerator and denominator by $4$:
$$\text{P}(S\cup A)=\frac{16÷4}{52÷4}=\frac{4}{13}$$