To determine the probability of drawing a face card (Jack, Queen, King) from a standard deck of cards, we need to follow these steps:
Understand the Composition of a Standard Deck: A standard deck of cards consists of 52 cards. These are divided into four suits: Hearts, Diamonds, Clubs, and Spades. Each suit has 13 cards, which include:
10 number cards (Ace through 10)
3 face cards: Jack, Queen, King
Determine the Total Number of Face Cards: Each suit has 3 face cards (Jack, Queen, King). Since there are four suits, the total number of face cards in the deck is:
Number of face cards = 3 face cards/suit × 4 suits = 12 face cards
Calculate the Probability: Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Number of possible outcomes (total cards in the deck) = 52
Number of favorable outcomes (total face cards) = 12
Probability of drawing a face card = \(\frac{12}{52}\)
Simplify the Probability: Simplifying \(\frac{12}{52}\):
Divide both the numerator and the denominator by their greatest common divisor (4):
\(\frac{12 \div 4}{52 \div 4} = \frac{3}{13}\)
Conclusion: Hence, the probability of drawing a face card from a standard deck of cards is \(\frac{3}{13}\).
Given the options, the correct answer is \(\frac{3}{13}\).