Question

One card is drawn from a well-shuffled deck of 52 cards. The probability of getting a face card is:

• A. $ \frac{1}{26} $
• B. $ \frac{3}{13} $
• C. $ \frac{3}{26} $
• D. $ \frac{1}{52} $

Hint:

To calculate probabilities involving a deck of cards, identify the number of favorable outcomes and divide by the total number of possible outcomes. Simplify fractions to match the given options.

Answer 1

The Correct Option is B

Step 1: Understand the Deck Composition.
A standard deck of 52 cards consists of:
4 suits (hearts, diamonds, clubs, spades).
Each suit has 13 cards: 2 through 10, Jack, Queen, King, and Ace.
The "face cards" are the Jack, Queen, and King of each suit.
Therefore, there are: \[ 3 \text{ face cards per suit} \times 4 \text{ suits} = 12 \text{ face cards in total}. \] Step 2: Calculate the Probability.
The probability of drawing a face card is given by: \[ P(\text{Face Card}) = \frac{\text{Number of Face Cards}}{\text{Total Number of Cards}} = \frac{12}{52}. \] Simplify the fraction: \[ P(\text{Face Card}) = \frac{12}{52} = \frac{3}{13}. \] Step 3: Analyze the Options.
Option (1): \( \frac{1}{26} \) — Incorrect, as this does not match the calculated value.
Option (2): \( \frac{3}{13} \) — Correct, as it matches the calculated value.
Option (3): \( \frac{3}{26} \) — Incorrect, as this does not match the calculated value.
Option (4): \( \frac{1}{52} \) — Incorrect, as this does not match the calculated value.
Step 4: Final Answer.
\[ (2) \quad \frac{3}{13} \]