medium difficulty4 min

Sample Space

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

In one line: Sample space is the full menu of outcomes.

Understand it

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

Example

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

Formula and rule

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

See it worked out

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

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 you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the sample space for tossing two coins together?

Think first, then show answer

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

Common wrong answer

For two coins, writing {H, T}.

Why it loses marks: It describes one coin, not two coins together.

Don't mix this up

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

Exam tip

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

Sample Space diagram

Open full screen to read every label clearly.

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

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

1
Enough for 1 mark
Sample space is the set or list of all possible outcomes of a random experiment.
2
Add for 2 marks
Example: For tossing one coin, the sample space is {H, T}. For rolling one die, it is {1, 2, 3, 4, 5, 6}.
3
Add for 3 marks
A correct sample space prevents wrong probability answers.

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