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Chance and Likelihood

Chance and likelihood describe how possible an event is, using words such as certain, impossible, likely, unlikely, and equally likely.

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Student-friendly explanation

Before writing probability as a number, students should judge the situation sensibly. If an event must happen, it is certain. If it cannot happen, it is impossible. If it has a better chance than another event, it is more likely.

How to write this in exams

  1. 1

    Start with the exact idea

    Chance and likelihood describe how possible an event is, using words such as certain, impossible, likely, unlikely, and equally likely.

  2. 2

    Then show how to use it

    Identify the event, check whether it can happen, compare favourable cases with other cases, and then choose the correct likelihood word.

  3. 3

    Add one concrete example

    Getting a number less than 7 on a normal die is certain, while getting 8 on the same die is impossible.

  4. 4

    Avoid this incomplete answer

    Calling blue impossible in a bag with 8 red and 2 blue balls is wrong because blue balls are present, though fewer.

Definition

Chance and likelihood describe how possible an event is, using words such as certain, impossible, likely, unlikely, and equally likely.

Example

Getting a number less than 7 on a normal die is certain, while getting 8 on the same die is impossible.

Rule to remember

Use language first: impossible means no chance, certain means must happen, likely means better chance, and unlikely means smaller chance.

Memory hook

Unlikely is not impossible; it only means less chance.

Examples and method

Worked example

For a bag with 8 red balls and 2 blue balls, picking a red ball is more likely than picking a blue ball because red balls are more in number.

Method to apply

Identify the event, check whether it can happen, compare favourable cases with other cases, and then choose the correct likelihood word.

Diagram support

A simple chance line from impossible to certain can help compare events in order.

How CBSE asks it

Questions may ask students to classify everyday events as certain, impossible, likely, or unlikely, with a short reason.

Avoid common mistakes

Common confusion

Students often call an event impossible just because it is unlikely. Unlikely means it can still happen, but with a small chance.

Common wrong answer

Calling blue impossible in a bag with 8 red and 2 blue balls is wrong because blue balls are present, though fewer.

Exam tip

Read the condition carefully and decide whether the event can happen, must happen, or may happen before assigning a probability idea.

Quick check

On a normal die, is getting an even number impossible, unlikely, likely, or certain?

Getting an even number on a normal die is likely but not certain, because 2, 4, and 6 are possible outcomes out of six total outcomes.

Answer writing and exam use

1-mark answer

Chance and likelihood describe how possible an event is, using words such as certain, impossible, likely, unlikely, and equally likely.

2-mark answer

Chance and likelihood describe how possible an event is, using words such as certain, impossible, likely, unlikely, and equally likely. Use language first: impossible means no chance, certain means must happen, likely means better chance, and unlikely means smaller chance. Getting a number less than 7 on a normal die is certain, while getting 8 on the same die is impossible.

3-mark answer

Before writing probability as a number, students should judge the situation sensibly. If an event must happen, it is certain. If it cannot happen, it is impossible. If it has a better chance than another event, it is more likely. Use language first: impossible means no chance, certain means must happen, likely means better chance, and unlikely means smaller chance. For a bag with 8 red balls and 2 blue balls, picking a red ball is more likely than picking a blue ball because red balls are more in number. Questions may ask students to classify everyday events as certain, impossible, likely, or unlikely, with a short reason. Calling blue impossible in a bag with 8 red and 2 blue balls is wrong because blue balls are present, though fewer.
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