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Impossible event

An impossible event is an event that cannot happen in a given experiment.

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Student-friendly explanation

If there are no favourable outcomes, the probability of the event is 0. Examples include getting 7 on a standard die or drawing a card of an impossible suit. The student should always check whether the event can actually occur before calculating anything else.

How to write this in exams

  1. 1

    Start with the exact idea

    An impossible event is an event that cannot happen in a given experiment.

  2. 2

    Then show how to use it

    1. Read the event carefully. 2. Check the sample space. 3. See whether any favourable outcome exists. 4. If none exists, write probability 0.

  3. 3

    Add one concrete example

    Getting a 7 on one throw of a standard die is impossible, so its probability is 0.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 1/6 for getting 7 on a die because the student knows a die has six faces but forgets to check the actual faces.

Definition

An impossible event is an event that cannot happen in a given experiment.

Example

Getting a 7 on one throw of a standard die is impossible, so its probability is 0.

Rule to remember

If an event has no favourable outcomes, then P(E) = 0.

Memory hook

No favourable outcome means zero probability.

Examples and method

Worked example

If a number card from 1 to 5 is chosen, getting 6 is impossible. Since there are no favourable outcomes, the probability is 0.

Method to apply

1. Read the event carefully. 2. Check the sample space. 3. See whether any favourable outcome exists. 4. If none exists, write probability 0.

Diagram support

A sample-space list helps show quickly that the required outcome is absent.

How CBSE asks it

Questions often ask whether an event is possible, impossible, or what its probability is when no favourable outcome exists.

Avoid common mistakes

Common confusion

Students sometimes write a small fraction for an impossible event instead of 0.

Common wrong answer

A common wrong answer is 1/6 for getting 7 on a die because the student knows a die has six faces but forgets to check the actual faces.

Exam tip

If the event has no favourable outcomes, stop and write probability 0.

Quick check

What is the probability of getting a 9 when one standard die is thrown?

It is 0 because a standard die has only the faces 1 to 6, so getting 9 cannot happen.

Answer writing and exam use

1-mark answer

An impossible event is an event that cannot happen in a given experiment.

2-mark answer

An impossible event is an event that cannot happen in a given experiment. If an event has no favourable outcomes, then P(E) = 0. Getting a 7 on one throw of a standard die is impossible, so its probability is 0.

3-mark answer

If there are no favourable outcomes, the probability of the event is 0. Examples include getting 7 on a standard die or drawing a card of an impossible suit. The student should always check whether the event can actually occur before calculating anything else. If an event has no favourable outcomes, then P(E) = 0. If a number card from 1 to 5 is chosen, getting 6 is impossible. Since there are no favourable outcomes, the probability is 0. Questions often ask whether an event is possible, impossible, or what its probability is when no favourable outcome exists. A common wrong answer is 1/6 for getting 7 on a die because the student knows a die has six faces but forgets to check the actual faces.
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