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

Problem:
A card is drawn at random from a well-shuffled standard deck of 52 playing cards. We are to find the probability that the card drawn is a red queen.

Step 1: Understand the structure of a deck
A standard deck of 52 playing cards consists of:
- 4 suits: Hearts (♥), Diamonds (♦), Clubs (♣), and Spades (♠)
- Each suit contains 13 cards: A, 2–10, J, Q, K
- Among these suits, Hearts and Diamonds are red-colored.

Therefore, there are two red queens in the entire deck:
- Queen of Hearts
- Queen of Diamonds

Step 2: Apply the formula for probability
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
- Number of favorable outcomes = 2 (red queens)
- Total number of outcomes = 52 (total cards in the deck)

\[ \text{Probability} = \frac{2}{52} = \frac{1}{26} \]

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