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Sample space for die throw

The sample space for throwing a die once is the set of all possible faces that can appear.

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Student-friendly explanation

A standard die has six faces marked 1, 2, 3, 4, 5, and 6. So the sample space for one throw is {1, 2, 3, 4, 5, 6}. This is one of the most basic sample spaces in Class 10 probability and is used again and again in exam questions.

How to write this in exams

  1. 1

    Start with the exact idea

    The sample space for throwing a die once is the set of all possible faces that can appear.

  2. 2

    Then show how to use it

    1. Recognise the object as a standard die. 2. Write all six face numbers. 3. Check that no number is missing. 4. Use the list for counting favourable outcomes.

  3. 3

    Add one concrete example

    For one die throw, the sample space is {1, 2, 3, 4, 5, 6}.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is {0, 1, 2, 3, 4, 5} because the student thinks counting starts from zero, which is not true for a die.

Definition

The sample space for throwing a die once is the set of all possible faces that can appear.

Example

For one die throw, the sample space is {1, 2, 3, 4, 5, 6}.

Rule to remember

For one standard die throw, S = {1, 2, 3, 4, 5, 6}.

Memory hook

A die has six faces, so the sample space has six numbers.

Examples and method

Worked example

If one die is thrown, the total number of possible outcomes is 6. Therefore, the probability of getting any one exact face, such as 4, is 1/6.

Method to apply

1. Recognise the object as a standard die. 2. Write all six face numbers. 3. Check that no number is missing. 4. Use the list for counting favourable outcomes.

Diagram support

A cube sketch with six numbered faces can help students remember the full sample space.

How CBSE asks it

Students may be asked to write the sample space, count outcomes, or find probability of a numbered face.

Avoid common mistakes

Common confusion

Students sometimes include 0 or forget one face when writing the sample space.

Common wrong answer

A common wrong answer is {0, 1, 2, 3, 4, 5} because the student thinks counting starts from zero, which is not true for a die.

Exam tip

For a single die, always write all six faces before starting any probability calculation.

Quick check

What is the sample space for one throw of a standard die?

The sample space is {1, 2, 3, 4, 5, 6}, because a standard die has six faces and any one of them can appear.

Answer writing and exam use

1-mark answer

The sample space for throwing a die once is the set of all possible faces that can appear.

2-mark answer

The sample space for throwing a die once is the set of all possible faces that can appear. For one standard die throw, S = {1, 2, 3, 4, 5, 6}. For one die throw, the sample space is {1, 2, 3, 4, 5, 6}.

3-mark answer

A standard die has six faces marked 1, 2, 3, 4, 5, and 6. So the sample space for one throw is {1, 2, 3, 4, 5, 6}. This is one of the most basic sample spaces in Class 10 probability and is used again and again in exam questions. For one standard die throw, S = {1, 2, 3, 4, 5, 6}. If one die is thrown, the total number of possible outcomes is 6. Therefore, the probability of getting any one exact face, such as 4, is 1/6. Students may be asked to write the sample space, count outcomes, or find probability of a numbered face. A common wrong answer is {0, 1, 2, 3, 4, 5} because the student thinks counting starts from zero, which is not true for a die.
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