Question:
One card is drawn at random from a well shuffled pack of 52 cards. The probability that the card drawn is a face card (Jack, Queen, and King only) is
One card is drawn at random from a well shuffled pack of 52 cards. The probability that the card drawn is a face card (Jack, Queen, and King only) is
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When calculating the probability of drawing specific cards, count the favorable cards across all suits and divide by the total number of cards in the deck.
Updated On: Jul 18, 2026
- \(\frac{1}{13}\)
- \(\frac{3}{13}\)
- \(\frac{1}{4}\)
- \(\frac{9}{52}\)
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The Correct Option is B
Solution and Explanation
Step 1: Total number of cards.
A standard deck contains 52 cards.
Step 2: Total number of face cards.
Each suit (hearts, diamonds, clubs, spades) has 3 face cards: Jack, Queen, King.
Total face cards \(= 3 \times 4 = 12\).
Step 3: Probability formula.
\[ P(\text{face card}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
Step 4: Apply numbers.
\[ P(\text{face card}) = \frac{12}{52} \]
Step 5: Simplify the fraction.
\[ \frac{12}{52} = \frac{3}{13} \]
Step 6: Final conclusion.
Hence, the probability of drawing a face card is \[ \boxed{\frac{3}{13}} \]
A standard deck contains 52 cards.
Step 2: Total number of face cards.
Each suit (hearts, diamonds, clubs, spades) has 3 face cards: Jack, Queen, King.
Total face cards \(= 3 \times 4 = 12\).
Step 3: Probability formula.
\[ P(\text{face card}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
Step 4: Apply numbers.
\[ P(\text{face card}) = \frac{12}{52} \]
Step 5: Simplify the fraction.
\[ \frac{12}{52} = \frac{3}{13} \]
Step 6: Final conclusion.
Hence, the probability of drawing a face card is \[ \boxed{\frac{3}{13}} \]
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