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

Let's solve this using probability rules for the union of two events:
P(S∪A)=P(S)+P(A)−P(S∩A)
Where:

S is the event of drawing a Spade. A standard deck contains 13 spades:

P(S)=
52
13
​

A is the event of drawing an Ace. A standard deck contains 4 aces:

P(A)=
52
4
​

S∩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:

P(S∩A)=
52
1
​

Substitute these values into the formula:

P(S∪A)=
52
13
​
+
52
4
​
−
52
1
​
=
52
13+4−1
​
=
52
16
​

Simplifying the fraction by dividing the numerator and denominator by 4:

P(S∪A)=
52÷4
16÷4
​
=
13
4
​