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Certain event

A certain event is an event that must happen in a given experiment.

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Student-friendly explanation

If an event always happens, its probability is 1. For example, when one standard die is thrown, getting a number less than 7 is certain because every face is less than 7. Students should connect certainty with full sample-space coverage, not with one special outcome.

How to write this in exams

  1. 1

    Start with the exact idea

    A certain event is an event that must happen in a given experiment.

  2. 2

    Then show how to use it

    1. Write the sample space. 2. Check whether every outcome satisfies the event. 3. If yes, the event is certain. 4. Write probability 1.

  3. 3

    Add one concrete example

    When a standard die is thrown once, getting a number less than 7 is a certain event.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 1/6 because the student thinks certainty must mean one favourable outcome, but certainty means all outcomes are favourable.

Definition

A certain event is an event that must happen in a given experiment.

Example

When a standard die is thrown once, getting a number less than 7 is a certain event.

Rule to remember

If an event includes every outcome of the sample space, then P(E) = 1.

Memory hook

All outcomes help the event happen, so probability is 1.

Examples and method

Worked example

For a die throw, the event 'getting a number from 1 to 6' includes all outcomes. So its probability is 1.

Method to apply

1. Write the sample space. 2. Check whether every outcome satisfies the event. 3. If yes, the event is certain. 4. Write probability 1.

Diagram support

A sample-space list with all outcomes highlighted helps show certainty very clearly.

How CBSE asks it

Exam questions may ask for the probability of an event that is guaranteed to occur or to identify a certain event.

Avoid common mistakes

Common confusion

Students sometimes think probability 1 means one outcome only, instead of an event that always happens.

Common wrong answer

A common wrong answer is 1/6 because the student thinks certainty must mean one favourable outcome, but certainty means all outcomes are favourable.

Exam tip

If every outcome in the sample space supports the event, the probability is 1.

Quick check

When one standard die is thrown, what is the probability of getting a number less than 7?

The probability is 1 because all six faces of the die are less than 7, so the event must happen.

Answer writing and exam use

1-mark answer

A certain event is an event that must happen in a given experiment.

2-mark answer

A certain event is an event that must happen in a given experiment. If an event includes every outcome of the sample space, then P(E) = 1. When a standard die is thrown once, getting a number less than 7 is a certain event.

3-mark answer

If an event always happens, its probability is 1. For example, when one standard die is thrown, getting a number less than 7 is certain because every face is less than 7. Students should connect certainty with full sample-space coverage, not with one special outcome. If an event includes every outcome of the sample space, then P(E) = 1. For a die throw, the event 'getting a number from 1 to 6' includes all outcomes. So its probability is 1. Exam questions may ask for the probability of an event that is guaranteed to occur or to identify a certain event. A common wrong answer is 1/6 because the student thinks certainty must mean one favourable outcome, but certainty means all outcomes are favourable.
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