A card is drawn at random from a standard deck of 52 playing cards. What is the probability that the card is either a queen or an ace?

Introduction / Context:
This problem involves drawing a single card from a standard deck and calculating the probability that it is either a queen or an ace. It is a typical example of probability with playing cards, testing knowledge of deck composition and use of basic probability formulas.

Given Data / Assumptions:

• A standard deck has 52 cards.
• There are 4 suits and each suit has 13 cards.
• There are 4 queens and 4 aces in the deck.
• No card is both a queen and an ace, so the two events are mutually exclusive.
• One card is drawn at random, and all cards are equally likely to be selected.

Concept / Approach:
We consider two mutually exclusive events: drawing a queen and drawing an ace. The probability that the drawn card is a queen or an ace is the sum of the probabilities of these two events, because they cannot happen simultaneously on a single card. We count how many cards belong to each category and divide by 52.

Step-by-Step Solution:
Number of queens in the deck = 4 (one in each suit). Number of aces in the deck = 4 (one in each suit). Since no card is simultaneously a queen and an ace, there is no overlap. Total favourable cards (queen or ace) = 4 + 4 = 8. Total cards in the deck = 52. Required probability = favourable / total = 8 / 52. Simplify 8 / 52 by dividing numerator and denominator by 4 to get 2 / 13.

Verification / Alternative check:
We can think in fractional terms: probability of a queen is 4/52 = 1/13, probability of an ace is also 4/52 = 1/13. Because the events are mutually exclusive, probability of queen or ace is 1/13 + 1/13 = 2/13. This confirms the earlier calculation based on counting favourable cards directly.

Why Other Options Are Wrong:
9/13 and 11/13: These are far too large for such a specific event and would suggest that most cards are queens or aces, which is not true.
4/13: This would imply 16 favourable cards, double the actual count of 8.
None of these: This is incorrect because the correct probability 2/13 is explicitly present as one of the options.

Common Pitfalls:
Some learners mistakenly include kings in the count or misremember the total number of each rank in a standard deck. Another frequent error is to forget to simplify the fraction 8/52, though leaving it unsimplified does not change its value. The most important conceptual point is recognizing that queen and ace are mutually exclusive outcomes for a single card, so their probabilities add directly.

Final Answer:
Thus, the probability that the drawn card is a queen or an ace is 2/13.