Question

A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a queen of spade is

• A. \(\frac{1}{26}\)
• B. \(\frac{1}{52}\)
• C. 0
• D. \(\frac{1}{4}\)

Hint:

Always read the card description carefully!
- If it asks for "a Queen", there are 4 queens, so the probability is \(\frac{4}{52} = \frac{1}{13}\).
- If it asks for "a spade", there are 13 spades, so the probability is \(\frac{13}{52} = \frac{1}{4}\).
- Since it asks for the unique "Queen of Spade", there is only 1 such card, so the probability is \(\frac{1}{52}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a standard probability question involving a deck of playing cards.
We need to calculate the probability of drawing a very specific card: the "Queen of Spades" from a well-shuffled deck of 52 playing cards.

Step 2: Key Formula or Approach:
The formula for probability of an event \(E\) is: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] We need to identify the total number of playing cards and how many of those cards fit the description of being a "Queen of Spades".

Step 3: Detailed Explanation:
1. Find the total number of possible outcomes:
A standard deck of playing cards has a total of 52 cards. \[ \text{Total outcomes} = 52 \] 2. Identify the number of favorable outcomes:
- A deck is divided into 4 suits: Spades, Hearts, Diamonds, and Clubs.
- Each suit has exactly one Queen.
- Therefore, there is only 1 Queen of Spades in the entire deck of 52 cards. \[ \text{Number of favorable outcomes} = 1 \] 3. Calculate the probability of drawing the Queen of Spades: \[ P(\text{Queen of Spades}) = \frac{1}{52} \]

Step 4: Final Answer:
The probability of getting a queen of spade is \(\frac{1}{52}\).
Therefore, the correct option is (B).