From a pack of 52 cards two are drawn with replacement. The probability, that the first is a diamond and the second is a king, is

Options

A. `1//26`
B. 17/2704
C. `1//52`
D. None of these

Answer

To find the probability that the first card drawn is a diamond and the second card drawn is a king, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We are drawing two cards from a deck of 52 cards with replacement. This means that after drawing the first card, we put it back into the deck before drawing the second card.

2. **Calculate the Probability of Drawing a Diamond**:
- In a standard deck of cards, there are 13 diamonds.
- The total number of cards in the deck is 52.
- Therefore, the probability of drawing a diamond (P(Diamond)) is:
\[ P(Diamond) = \frac{\text{Number of Diamonds}}{\text{Total Number of Cards}} = \frac{13}{52} = \frac{1}{4} \]

3. **Calculate the Probability of Drawing a King**:
- There are 4 kings in a standard deck of cards.
- The total number of cards remains 52 since we are drawing with replacement.
- Therefore, the probability of drawing a king (P(King)) is:
\[ P(King) = \frac{\text{Number of Kings}}{\text{Total Number of Cards}} = \frac{4}{52} = \frac{1}{13} \]

4. **Calculate the Combined Probability**:
- Since the two events (drawing a diamond first and drawing a king second) are independent, we can multiply their probabilities:
\[ P(Diamond \text{ and } King) = P(Diamond) \times P(King) = \frac{1}{4} \times \frac{1}{13} = \frac{1}{52} \]

5. **Final Answer**: The probability that the first card drawn is a diamond and the second card drawn is a king is:
\[ \frac{1}{52} \]