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Probability in card selection contexts

This is the use of probability when one or more cards are chosen from a deck or a card set.

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Student-friendly explanation

Card questions test careful counting of suits, colours, and ranks. In a standard deck of 52 cards, there are 4 suits and 13 cards in each suit. Students should remember that probabilities depend on the exact property asked, such as a heart, a face card, or an ace.

How to write this in exams

  1. 1

    Start with the exact idea

    This is the use of probability when one or more cards are chosen from a deck or a card set.

  2. 2

    Then show how to use it

    1. Identify the exact card property asked. 2. Count favourable cards. 3. Count total cards, usually 52. 4. Divide and simplify.

  3. 3

    Add one concrete example

    The probability of drawing a heart from a standard deck is 13/52 = 1/4.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 1/4 for a queen because the student confuses queens with suits and ignores the four separate queens.

Definition

This is the use of probability when one or more cards are chosen from a deck or a card set.

Example

The probability of drawing a heart from a standard deck is 13/52 = 1/4.

Rule to remember

Probability = favourable cards / total cards, after identifying the exact card group asked.

Memory hook

Suit, colour, or rank: count the right group first.

Examples and method

Worked example

In a deck, there are 26 red cards out of 52 total cards. So the probability of drawing a red card is 26/52 = 1/2.

Method to apply

1. Identify the exact card property asked. 2. Count favourable cards. 3. Count total cards, usually 52. 4. Divide and simplify.

Diagram support

A quick deck table by suit or rank helps organise the favourable cards correctly.

How CBSE asks it

Questions usually ask for probability of a suit, colour, face card, ace, or king from a standard deck.

Avoid common mistakes

Common confusion

Students often confuse a suit with a rank and count too many or too few cards.

Common wrong answer

A common wrong answer is 1/4 for a queen because the student confuses queens with suits and ignores the four separate queens.

Exam tip

For card problems, first decide whether the question asks about suit, colour, rank, or face card.

Quick check

From a standard deck of 52 cards, what is the probability of drawing a queen?

There are 4 queens in a deck of 52 cards, so the probability is 4/52, which simplifies to 1/13.

Answer writing and exam use

1-mark answer

This is the use of probability when one or more cards are chosen from a deck or a card set.

2-mark answer

This is the use of probability when one or more cards are chosen from a deck or a card set. Probability = favourable cards / total cards, after identifying the exact card group asked. The probability of drawing a heart from a standard deck is 13/52 = 1/4.

3-mark answer

Card questions test careful counting of suits, colours, and ranks. In a standard deck of 52 cards, there are 4 suits and 13 cards in each suit. Students should remember that probabilities depend on the exact property asked, such as a heart, a face card, or an ace. Probability = favourable cards / total cards, after identifying the exact card group asked. In a deck, there are 26 red cards out of 52 total cards. So the probability of drawing a red card is 26/52 = 1/2. Questions usually ask for probability of a suit, colour, face card, ace, or king from a standard deck. A common wrong answer is 1/4 for a queen because the student confuses queens with suits and ignores the four separate queens.
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