One card is drawn at random from a standard pack of 52 playing cards. What is the probability that the card drawn is a face card (that is, a Jack, Queen or King)?

Introduction / Context: This is a basic card probability question that focuses on counting specific types of cards, called face cards. It tests your knowledge of the composition of a standard 52 card deck and the ability to express the chance of drawing one of these special cards as a fraction.

Given Data / Assumptions:

• Standard deck size = 52 cards.
• Four suits: hearts, diamonds, clubs and spades.
• Each suit has 3 face cards: Jack, Queen and King.
• Total face cards in the deck = 4 * 3 = 12.
• One card is drawn at random.

Concept / Approach: Since all 52 cards are equally likely, the probability of drawing a face card is the number of face cards divided by the total number of cards. We simply count the favourable cards and use the classical probability formula P(event) = favourable outcomes / total outcomes.

Step-by-Step Solution: Number of face cards per suit = 3 (Jack, Queen, King). Number of suits = 4. Total face cards = 3 * 4 = 12. Total cards in deck = 52. Probability of drawing a face card = 12 / 52. Simplify 12 / 52 by dividing numerator and denominator by 4: 12 / 52 = 3 / 13.

Verification / Alternative check: We can also think in terms of suits. The probability that the card is a face card from hearts is 3/52, and similarly 3/52 for each of the other three suits. Summing these four equal probabilities gives 4 * 3/52 = 12/52 = 3/13, which confirms the result.

Why Other Options Are Wrong: 1/13 corresponds to only 4 favourable cards, not the 12 face cards. 3/52 equals the probability that the card is a face card of a specific suit only, such as face card of hearts. 9/52 would imply 9 face cards total, which is not correct for a standard deck.

Common Pitfalls: Sometimes learners confuse face cards with all picture cards including Ace, but Ace is not considered a face card in most probability questions unless explicitly stated. Counting all ranks from Jack to Ace would lead to an incorrect favourable count.

Final Answer: Thus, the probability that the drawn card is a face card is 3/13.