Read the following text and answer the following question on the basis of the same.
On a weekend Rani was playing cards with her family. The deck has 52 cards. If her brother drew one card.
Find the probability of getting a red face card

Options

A. `(3)/(13)`
B. `(1)/(13)`
C. `(1)/(52)`
D. `(3)/(26)`

Answer

To find the probability of drawing a red face card from a standard deck of 52 cards, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total number of cards in the deck**:
- A standard deck of cards has 52 cards.

2. **Determine the total number of face cards**:
- In a deck, there are 3 face cards (Jack, Queen, King) in each suit.
- Since there are 4 suits (hearts, diamonds, clubs, spades), the total number of face cards is:
\[ 3 \text{ face cards/suit} \times 4 \text{ suits} = 12 \text{ face cards} \]

3. **Identify the red face cards**:
- The red suits are hearts and diamonds.
- Each red suit has 3 face cards (Jack, Queen, King).
- Therefore, the total number of red face cards is:
\[ 3 \text{ face cards (hearts)} + 3 \text{ face cards (diamonds)} = 6 \text{ red face cards} \]

4. **Calculate the probability of drawing a red face card**:
- The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes (red face cards) is 6, and the total number of outcomes (total cards) is 52.
- Thus, the probability is:
\[ P(\text{red face card}) = \frac{6}{52} \]

5. **Simplify the fraction**:
- To simplify \( \frac{6}{52} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{6 \div 2}{52 \div 2} = \frac{3}{26} \]

### Final Answer:
The probability of drawing a red face card is \( \frac{3}{26} \).