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Sample Space

Sample space is the set or list of all possible outcomes of a random experiment.

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Student-friendly explanation

A correct sample space prevents wrong probability answers. For simple experiments, list every outcome once and make sure no possible result is left out.

How to write this in exams

  1. 1

    Start with the exact idea

    Sample space is the set or list of all possible outcomes of a random experiment.

  2. 2

    Then show how to use it

    Identify each stage, list all outcomes for each stage, combine systematically, and count the complete list.

  3. 3

    Add one concrete example

    For tossing one coin, the sample space is {H, T}. For rolling one die, it is {1, 2, 3, 4, 5, 6}.

  4. 4

    Avoid this incomplete answer

    For two coins, writing {H, T} is wrong because it describes one coin, not two coins together.

Definition

Sample space is the set or list of all possible outcomes of a random experiment.

Example

For tossing one coin, the sample space is {H, T}. For rolling one die, it is {1, 2, 3, 4, 5, 6}.

Rule to remember

Total outcomes in theoretical probability are counted from the sample space.

Memory hook

Sample space is the full menu of outcomes.

Examples and method

Worked example

For tossing one coin and rolling one die, sample outcomes include H1, H2, ..., H6, T1, T2, ..., T6, so there are 12 outcomes.

Method to apply

Identify each stage, list all outcomes for each stage, combine systematically, and count the complete list.

Diagram support

For two-stage experiments, a table or tree diagram can help list outcomes systematically.

How CBSE asks it

Students may be asked to write the sample space and then find probability of a selected event from it.

Avoid common mistakes

Common confusion

Students sometimes list only favourable outcomes and call that the sample space.

Common wrong answer

For two coins, writing {H, T} is wrong because it describes one coin, not two coins together.

Exam tip

Write the sample space before solving probability questions where two conditions or two stages are involved.

Quick check

What is the sample space for tossing two coins together?

The sample space is {HH, HT, TH, TT}, because each coin can show head or tail and order of the two coins is counted.

Study the sample space diagram carefully

Use the labelled diagram to keep sample space clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of sample space in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on sample space.

Revision cue

Revise sample space through the labels before writing the answer.

Answer writing and exam use

1-mark answer

Sample space is the set or list of all possible outcomes of a random experiment.

2-mark answer

Sample space is the set or list of all possible outcomes of a random experiment. Total outcomes in theoretical probability are counted from the sample space. For tossing one coin, the sample space is {H, T}. For rolling one die, it is {1, 2, 3, 4, 5, 6}.

3-mark answer

A correct sample space prevents wrong probability answers. For simple experiments, list every outcome once and make sure no possible result is left out. Total outcomes in theoretical probability are counted from the sample space. For tossing one coin and rolling one die, sample outcomes include H1, H2, ..., H6, T1, T2, ..., T6, so there are 12 outcomes. Students may be asked to write the sample space and then find probability of a selected event from it. For two coins, writing {H, T} is wrong because it describes one coin, not two coins together.
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