If a card is drawn from a well shuffled pack of 52 cards, then the probability that is a queen card is

Options

A. `(3)/(13)`
B. `(1)/(13)`
C. `(4)/(13)`
D. `(2)/(13)`

Answer

To solve the problem of finding the probability of drawing a queen card from a well-shuffled pack of 52 cards, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Number of Cards**:
A standard deck of playing cards consists of 52 cards.

2. **Identify the Total Number of Queens**:
In a standard deck, there are 4 suits: hearts, diamonds, clubs, and spades. Each suit contains one queen. Therefore, the total number of queen cards in the deck is:
\[ \text{Total Queens} = 1 \text{ (heart)} + 1 \text{ (diamond)} + 1 \text{ (club)} + 1 \text{ (spade)} = 4 \]

3. **Calculate the Probability**:
Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case:
- Favorable outcomes (drawing a queen) = 4
- Total possible outcomes (drawing any card) = 52

Thus, the probability \( P \) of drawing a queen card is given by:
\[ P(\text{Queen}) = \frac{\text{Number of Queens}}{\text{Total Number of Cards}} = \frac{4}{52} \]

4. **Simplify the Probability**:
We can simplify \( \frac{4}{52} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
\[ P(\text{Queen}) = \frac{4 \div 4}{52 \div 4} = \frac{1}{13} \]

5. **Final Answer**:
Therefore, the probability that the card drawn is a queen is:
\[ \boxed{\frac{1}{13}} \]