Question

Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the probability that both cards are queens is

• A. \( \frac{1}{221} \)
• B. \( \frac{1}{220} \)
• C. \( \frac{3}{220} \)
• D. \( \frac{2}{221} \)

Hint:

For probability problems involving cards, always start by calculating the total number of possible outcomes and the favorable outcomes, then compute the probability as a ratio.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
In a standard deck of 52 playing cards, there are 4 queens. When two cards are drawn without replacement, we are asked to find the probability that both cards are queens.

Step 2: Probability calculation.
The total number of ways to select 2 cards from 52 is \( \binom{52}{2} = \frac{52 \times 51}{2} = 1326 \). The number of ways to select 2 queens from 4 is \( \binom{4}{2} = \frac{4 \times 3}{2} = 6 \). Thus, the probability that both cards are queens is: \[ P(\text{both queens}) = \frac{6}{1326} = \frac{1}{221}. \]
Step 3: Conclusion.
Therefore, the correct answer is option (A) \( \frac{1}{221} \).