medium difficulty5 min

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.

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

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

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

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

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.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
This is the use of probability when one or more cards are chosen from a deck or a card set.
2
Add for 2 marks
Example: The probability of drawing a heart from a standard deck is 13/52 = 1/4.
3
Add for 3 marks
In a standard deck of 52 cards, there are 4 suits and 13 cards in each suit.

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