If a card is drawn at random from a pack of 52 cards, what is the chance of…

For two events A and B that can overlap, the probability of "A or B" follows the inclusion-exclusion principle: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). The overlap term is subtracted because outcomes belonging to both events would otherwise be counted twice.

1. Let A = drawing a Diamond and B = drawing an Ace, from a standard 52-card deck.

2. Count each event: number of Diamonds = 13, number of Aces = 4.

3. Find the overlap: the Ace of Diamonds belongs to both groups, so the overlap count = 1.

4. Favourable outcomes for "Diamond or Ace" = 13 + 4 − 1 = 16.

5. Probability = 16/52, which simplifies to 4/13.

Cross-check by counting directly without double counting: 12 diamonds that are not aces, plus all 4 aces (including the Ace of Diamonds), gives 12 + 4 = 16 cards — the same favourable count, confirming 4/13.