A card is drawn at random from a standard 52-card deck. What is the probability of drawing a queen or a spade?

Step 1: Identify the two events.

Let Q represent drawing a queen.
Let S represent drawing a spade.

There are 4 queens in a standard deck and 13 spades.

Step 2: Identify the overlap between the events.

The queen of spades is both a queen and a spade.

If we simply add 4 + 13, the queen of spades would be counted twice.

Step 3: Use the addition rule.

P(Q or S) = P(Q) + P(S) - P(Q and S)

Using counts, the number of favorable cards is:
4 + 13 - 1 = 16

Step 4: Divide by the total number of cards.

P(Q or S) = 16/52

Step 5: Simplify the fraction.

16/52 = 4/13

As a decimal:
4/13 ≈ 0.3077

Therefore, the probability of drawing a queen or a spade is 4/13, or approximately 0.3077.