From a standard 52-card deck, what is the probability that a randomly drawn card is a diamond or a king?

Introduction / Context:We compute a simple union of two card events: “diamond” or “king”. Since one card (king of diamonds) lies in both sets, inclusion–exclusion is needed to avoid double-counting.

Given Data / Assumptions:

• Diamonds = 13 cards.
• Kings = 4 cards.
• Overlap = 1 card (king of diamonds).
• Total cards = 52.

Concept / Approach:P(diamond ∪ king) = (13 + 4 − 1)/52 = 16/52. Reduce the fraction to simplest terms.

Step-by-Step Solution:

Verification / Alternative check:Complementary event is “not diamond and not king” = 39/52; thus union is 1 − 39/52 = 13/52? Careful: “not diamond and not king” equals 52 − (diamonds ∪ kings) = 36; hence union is 16/52 = 4/13, matching above.

Why Other Options Are Wrong:4/52 is only diamonds OR only kings if miscounted; 2/13 undercounts; 1/52 is just a single card.

Common Pitfalls:Double-counting the king of diamonds by simply adding 13 + 4 without subtracting the overlap.

Final Answer:4/13