The probability of drawing a face card from a standard pack of 52 cards is

Options

A. `(4)/(13)`
B. `(1)/(13)`
C. `(3)/(13)`
D. `(10)/(13)`

Answer

To find the probability of drawing a face card from a standard pack of 52 cards, follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Cards:**
A standard deck of cards contains 52 cards.

2. **Identify the Face Cards:**
The face cards in a deck are the King, Queen, and Jack. Each suit (hearts, diamonds, clubs, and spades) has one of each face card.

3. **Calculate the Total Number of Face Cards:**
Since there are 4 suits and each suit has 3 face cards, the total number of face cards is:
\[ \text{Total Face Cards} = 3 \text{ (face cards per suit)} \times 4 \text{ (suits)} = 12 \]

4. **Calculate the Probability:**
The probability \( P \) of drawing a face card can be calculated using the formula:
\[ P(\text{face card}) = \frac{\text{Number of Face Cards}}{\text{Total Number of Cards}} = \frac{12}{52} \]

5. **Simplify the Fraction:**
To simplify \( \frac{12}{52} \), divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[ \frac{12 \div 4}{52 \div 4} = \frac{3}{13} \]

6. **Final Answer:**
Therefore, the probability of drawing a face card from a standard pack of 52 cards is:
\[ \frac{3}{13} \]