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: Identify the total number of outcomes.
A standard deck has 52 playing cards. So total outcomes \(= 52\).
Step 2: Identify the favourable outcomes.
We want to draw the Queen of Spades. There is exactly 1 such card in the deck.
Step 3: Apply the probability formula.
\(P(\text{Queen of Spades}) = \frac{1}{52}\).
Step 4: Verify by elimination.
\(\frac{1}{26}\) would be the probability if there were 2 such cards. \(\frac{1}{4}\) is the probability of any queen (4 queens in 52 cards). \(\frac{1}{52}\) is the only correct value for one specific card.
Step 5: Confirm the answer.
There is one and only one Queen of Spades in a 52-card deck.
Step 6: Select the correct option.
Option 2 is \(\frac{1}{52}\).
\[ \boxed{\dfrac{1}{52}} \]