If a card is selected from a deck of 52 cards, then the probability of a being a red face card is

Options

A. `(3)/(26)`
B. `(3)/(13)`
C. `(2)/(13)`
D. `(1)/(2)`

Explanation

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

### Step 1: Understand the Composition of the Deck
A standard deck of cards contains 52 cards, which are divided into four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards.

### Step 2: Identify the Red Suits
The red suits in a deck are:
- Hearts
- Diamonds

### Step 3: Identify the Face Cards
Face cards are the Jack, Queen, and King. Each suit has one of each face card:
- Jack
- Queen
- King

### Step 4: Count the Red Face Cards
In the red suits (hearts and diamonds), the face cards are:
- Jack of Hearts
- Queen of Hearts
- King of Hearts
- Jack of Diamonds
- Queen of Diamonds
- King of Diamonds

Thus, there are a total of 6 red face cards.

### Step 5: Calculate the Total Number of Cards
The total number of cards in the deck is 52.

### Step 6: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case, the number of favorable outcomes (red face cards) is 6, and the total number of outcomes (total cards) is 52.

So, the probability \( P \) of selecting a red face card is:
\[ P(\text{red face card}) = \frac{6}{52} \]

### Step 7: Simplify the Probability
We can simplify \( \frac{6}{52} \) by dividing both the numerator and the denominator by 2:
\[ P(\text{red face card}) = \frac{3}{26} \]

### Final Answer
The probability of selecting a red face card from a deck of 52 cards is \( \frac{3}{26} \).

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