Question

A card is drawn from a well-shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is:

• A. \(\frac{1}{13}\)
• B. \(\frac{2}{13}\)
• C. \(\frac{1}{52}\)
• D. \(\frac{1}{26}\)

Answer 1

The Correct Option is D

Step 1: Understanding the problem:
We are asked to find the probability of drawing a red queen from a well-shuffled deck of 52 playing cards.
A standard deck of 52 playing cards consists of 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards, including one queen.
The red suits are hearts and diamonds. Therefore, the red queens are the queen of hearts and the queen of diamonds.

Step 2: Number of favorable outcomes:
There are two red queens in a standard deck of cards: the queen of hearts and the queen of diamonds. Hence, the number of favorable outcomes (drawing a red queen) is 2.

Step 3: Total number of outcomes:
Since the deck contains 52 cards, the total number of possible outcomes (total number of cards) is 52.

Step 4: Calculating the probability:
The probability of an event is the ratio of favorable outcomes to the total number of outcomes. Therefore, the probability of drawing a red queen is:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{52} \] Simplifying the fraction:
\[ \text{Probability} = \frac{1}{26} \]

Step 5: Conclusion:
The probability that the drawn card is a red queen is \( \frac{1}{26} \).