GCSE Maths Practice: listing-outcomes

Understanding Possible Outcomes in a Deck of Cards

This question focuses on identifying valid outcomes when drawing a single card from a standard deck of 52 cards. In probability, it is essential to understand the sample space — the complete set of all possible outcomes. For a deck of cards, the sample space is made up of every unique card in the deck. Knowing what cards exist in a standard deck helps lay the foundation for more advanced card probability questions later on.

A standard deck contains 52 cards, divided into four suits: Clubs, Diamonds, Hearts, and Spades. Each suit contains exactly 13 ranks: Ace, 2 through 10, Jack, Queen, and King. Because each of the 52 cards is different, drawing any specific card is considered a single, unique outcome. When you draw one card from the deck, you have 52 possible outcomes, one for each card.

Why All Listed Cards Are Valid Outcomes

In this question, the listed cards are the Ace of Spades, Queen of Hearts, and King of Clubs. These are all real, distinct cards that exist in a standard deck. None of them contain formatting errors or imaginary card names, and none require special rules. Cards such as the “Red Joker” or “14 of Hearts” would be invalid because they are not included in a standard deck. However, the cards listed here each belong to one of the four suits and one of the 13 ranks, making them fully valid outcomes.

Step-by-Step Reasoning

1. Recall that a standard deck contains 52 unique cards.
2. Identify the suits: Spades, Hearts, Clubs, Diamonds.
3. Recall the 13 ranks in each suit: Ace, 2–10, Jack, Queen, King.
4. Check if the listed cards belong to one of these suits and ranks.
5. Confirm that each card appears exactly once in the deck.

Because each option matches a valid rank-suit combination, all must be selected.

Worked Example 1: Spotting an Invalid Card

If the question listed a card like “11 of Spades”, it would be invalid because there is no rank 11 in a deck. Similarly, “King of Stars” would be impossible because Stars is not a suit. Understanding what makes cards valid helps eliminate impossible outcomes.

Worked Example 2: Drawing a Face Card

The face cards are Jack, Queen, and King. If asked whether the “Queen of Hearts” is a possible outcome when drawing a card, the answer would be yes because it is one of the 12 face cards found in the deck.

Worked Example 3: Drawing an Ace

The deck includes four Aces — one for each suit. The Ace of Spades is one of them. Therefore, drawing the Ace of Spades is always a possible outcome as long as the deck is complete.

Common Mistakes

• Thinking a deck includes Jokers. Standard probability questions assume a 52-card deck unless stated otherwise.
• Believing each suit has different numbers of cards. All suits contain exactly 13 cards.
• Mixing up suits and ranks. Both must be valid for the card to be valid.
• Assuming repeated cards exist. Each card appears exactly once.

Real-Life Applications

Understanding card decks is useful not only for probability exercises but also for strategy-based card games, computing simulations involving random selection, and probability experiments. In gaming and statistics, card-based probability provides a clear, structured example of a finite probability space.

FAQ

Q: How many possible outcomes exist when drawing one card?
A: There are 52 — one for each card.

Q: Are Jokers included?
A: Not in a standard deck used for Maths probability questions.

Q: Can multiple listed answers be correct?
A: Yes. If all options represent real cards, all are correct.

Study Tip

Memorise the structure of a standard deck — 4 suits × 13 ranks — to quickly recognise valid outcomes in card probability questions.