medium difficulty5 min

Certain event

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

In one line: All outcomes help the event happen, so probability is 1.

Understand it

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.

Example

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

Formula and rule

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

See it worked out

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

Worked example

1For a die throw, the event 'getting a number from 1 to 6' includes all outcomes.
2So its probability is 1.

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

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.

Don't mix this up

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

Exam tip

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

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

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

1
Enough for 1 mark
A certain event is an event that must happen in a given experiment.
2
Add for 2 marks
Example: When a standard die is thrown once, getting a number less than 7 is a certain event.
3
Add for 3 marks
If an event always happens, its probability is 1.

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