medium difficulty5 min

Impossible event

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

In one line: No favourable outcome means zero probability.

Understand it

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.

Example

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

Formula and rule

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

See it worked out

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

Worked example

1If a number card from 1 to 5 is chosen, getting 6 is impossible.
2Since there are no favourable outcomes, the probability is 0.

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

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.

Don't mix this up

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

Exam tip

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

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

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

1
Enough for 1 mark
An impossible event is an event that cannot happen in a given experiment.
2
Add for 2 marks
Example: Getting a 7 on one throw of a standard die is impossible, so its probability is 0.
3
Add for 3 marks
If there are no favourable outcomes, the probability of the event is 0.

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