Two cards are drawn from a well shuffled deck of 52 cards.The probability that one is red card and the other is a queen.

Options

A. `4//51`
B. `16//221`
C. `50//663`
D. none of these

Answer

To find the probability that one card drawn is a red card and the other is a queen from a well-shuffled deck of 52 cards, we can break down the problem into manageable steps.

### Step-by-Step Solution:

1. **Identify the Total Number of Cards**:
- A standard deck has 52 cards.

2. **Identify the Number of Red Cards**:
- There are 26 red cards in a deck (13 hearts and 13 diamonds).

3. **Identify the Number of Queens**:
- There are 4 queens in a deck (one from each suit: hearts, diamonds, clubs, and spades).

4. **Calculate the Probability for Two Scenarios**:
- We need to consider two scenarios:
- **Scenario 1**: The first card drawn is a red card, and the second card drawn is a queen.
- **Scenario 2**: The first card drawn is a queen, and the second card drawn is a red card.

5. **Calculate Probability for Scenario 1**:
- The probability of drawing a red card first:
\[ P(R_1) = \frac{26}{52} = \frac{1}{2} \]
- After drawing a red card, there are now 51 cards left in the deck, including 4 queens.
- The probability of drawing a queen second:
\[ P(Q_2 | R_1) = \frac{4}{51} \]
- Thus, the combined probability for Scenario 1 is:
\[ P(R_1 \text{ and } Q_2) = P(R_1) \times P(Q_2 | R_1) = \frac{1}{2} \times \frac{4}{51} = \frac{2}{51} \]

6. **Calculate Probability for Scenario 2**:
- The probability of drawing a queen first:
\[ P(Q_1) = \frac{4}{52} = \frac{1}{13} \]
- After drawing a queen, there are now 51 cards left, including 26 red cards.
- The probability of drawing a red card second:
\[ P(R_2 | Q_1) = \frac{26}{51} \]
- Thus, the combined probability for Scenario 2 is:
\[ P(Q_1 \text{ and } R_2) = P(Q_1) \times P(R_2 | Q_1) = \frac{1}{13} \times \frac{26}{51} = \frac{2}{51} \]

7. **Combine the Probabilities of Both Scenarios**:
- The total probability of drawing one red card and one queen is the sum of the probabilities of both scenarios:
\[ P(\text{one red and one queen}) = P(R_1 \text{ and } Q_2) + P(Q_1 \text{ and } R_2 = \frac{2}{51} + \frac{2}{51} = \frac{4}{51} \]

### Final Answer:
The probability that one card is a red card and the other is a queen is:
\[ \frac{4}{51} \]