A single card is drawn uniformly at random from a standard 52-card deck. What is the probability that it is neither a heart nor a king?

Introduction / Context:Use inclusion–exclusion to avoid double-counting the king of hearts when excluding hearts and kings from a deck. Then divide by total cards for the probability.

Given Data / Assumptions:

• 52-card standard deck.
• Hearts = 13; Kings = 4; overlap (king of hearts) = 1.

Concept / Approach:

• Cards that are heart or king = 13 + 4 − 1 = 16 (by inclusion–exclusion).
• “Neither” count = 52 − 16 = 36.
• Probability = 36/52 = 9/13.

Step-by-Step Solution:

Verification / Alternative check:Complement method directly: P(neither) = 1 − P(heart ∪ king) = 1 − 16/52 = 36/52 = 9/13.

Why Other Options Are Wrong:

• 4/13 and 2/13 correspond to the complement or partial counts.
• Duplicate 4/13 remains incorrect; “None of these” is false because 9/13 is correct.

Common Pitfalls:

• Double-counting the king of hearts if adding 13 and 4 without subtracting 1.

Final Answer:9/13