A card is drawn at random form a well - shuffled pack of 52 cards . The probability that the cards drawn is a diamond is ………….

Options

A. `(1)/(52)`
B. `(13)/(52)`
C. `(26)/(52)`
D. `(39)/(52)`

Answer

To find the probability that a card drawn at random from a well-shuffled pack of 52 cards is a diamond, we can 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 Number of Diamond Cards**:
In a standard deck, there are 4 suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. Therefore, the number of diamond cards in the deck is 13.

3. **Calculate the Probability**:
Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Favorable outcomes (drawing a diamond) = 13 (the number of diamond cards)
- Total outcomes (total number of cards) = 52

Thus, the probability \( P \) of drawing a diamond card is calculated as follows:
\[ P(\text{diamond}) = \frac{\text{Number of diamond cards}}{\text{Total number of cards}} = \frac{13}{52} \]

4. **Simplify the Fraction**:
To simplify \( \frac{13}{52} \), we divide both the numerator and the denominator by their greatest common divisor, which is 13:
\[ \frac{13 \div 13}{52 \div 13} = \frac{1}{4} \]

5. **Conclusion**:
Therefore, the probability that the card drawn is a diamond is \( \frac{1}{4} \).

### Final Answer:
The probability that the card drawn is a diamond is \( \frac{1}{4} \).

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