Single draw from a 52-card deck. What is the probability that the card is neither a heart nor a king?

Introduction / Context:We want the complement of “heart or king”. Use inclusion–exclusion to find the union first, then subtract from 1.

Given Data / Assumptions:

• Hearts = 13 cards.
• Kings = 4 cards.
• Overlap (king of hearts) = 1 card.

Concept / Approach:P(neither) = 1 − P(heart ∪ king). Compute the union via counts.

Step-by-Step Solution:Favorable for union = 13 + 4 − 1 = 16.P(heart ∪ king) = 16/52 = 4/13.Therefore P(neither) = 1 − 4/13 = 9/13.

Verification / Alternative check:Direct count of “neither” = 52 − 16 = 36 → 36/52 = 9/13.

Why Other Options Are Wrong:4/13 is the union, not the complement; 2/13 and 5/13 do not match the correct count.

Common Pitfalls:Double-counting the king of hearts or forgetting to subtract overlap.

Final Answer:9/13