Question

The probability of drawing a face card (Jack, Queen, King) from a standard deck of cards is

• A. $1/13$
• B. $3/13$
• C. $1/26$
• D. $3/52$

Hint:

Face cards include only J, Q, K — not Ace.

Answer 1

The Correct Option is B

To determine the probability of drawing a face card (Jack, Queen, King) from a standard deck of cards, we need to follow these steps:

1. 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
2. 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
3. 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 = \(\frac{12}{52}\)
4. Simplify the Probability: Simplifying \(\frac{12}{52}\):
   • Divide both the numerator and the denominator by their greatest common divisor (4):
     • \(\frac{12 \div 4}{52 \div 4} = \frac{3}{13}\)
5. 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 \(\frac{3}{13}\).