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Equally likely outcomes

Equally likely outcomes are outcomes that have the same chance of happening in an experiment.

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Student-friendly explanation

This idea is very important because the basic probability formula works properly only when outcomes are equally likely. A fair coin has H and T with the same chance, and a fair die has 1 to 6 with the same chance. If the object is biased, the simple formula may not be valid in the same direct way.

How to write this in exams

  1. 1

    Start with the exact idea

    Equally likely outcomes are outcomes that have the same chance of happening in an experiment.

  2. 2

    Then show how to use it

    1. Check whether the experiment is fair. 2. List all possible outcomes. 3. Compare whether each outcome has the same chance. 4. If yes, use the usual probability formula.

  3. 3

    Add one concrete example

    In a fair die throw, each face from 1 to 6 has the same chance, so the outcomes are equally likely.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is saying outcomes are equally likely only because there are two outcomes, while fairness is actually the deciding point.

Definition

Equally likely outcomes are outcomes that have the same chance of happening in an experiment.

Example

In a fair die throw, each face from 1 to 6 has the same chance, so the outcomes are equally likely.

Rule to remember

Equal likelihood means each outcome has the same chance, so probability counting can be used directly only then.

Memory hook

Same chance means equally likely.

Examples and method

Worked example

A fair coin is tossed once. The outcomes H and T each have chance 1/2, so they are equally likely. This is why probability of head is 1/2.

Method to apply

1. Check whether the experiment is fair. 2. List all possible outcomes. 3. Compare whether each outcome has the same chance. 4. If yes, use the usual probability formula.

Diagram support

A probability tree or outcome table helps show that each outcome has the same chance.

How CBSE asks it

Students may be asked to identify whether an experiment is fair or to decide if the outcomes are equally likely.

Avoid common mistakes

Common confusion

Students sometimes call outcomes equally likely just because there are many outcomes, even when the object is biased.

Common wrong answer

A common wrong answer is saying outcomes are equally likely only because there are two outcomes, while fairness is actually the deciding point.

Exam tip

Always ask first: is the coin, die, or spinner fair before applying the counting formula?

Quick check

Why are the faces of a fair die called equally likely outcomes?

They are called equally likely because each face has the same chance of appearing when the die is fair and thrown properly.

Answer writing and exam use

1-mark answer

Equally likely outcomes are outcomes that have the same chance of happening in an experiment.

2-mark answer

Equally likely outcomes are outcomes that have the same chance of happening in an experiment. Equal likelihood means each outcome has the same chance, so probability counting can be used directly only then. In a fair die throw, each face from 1 to 6 has the same chance, so the outcomes are equally likely.

3-mark answer

This idea is very important because the basic probability formula works properly only when outcomes are equally likely. A fair coin has H and T with the same chance, and a fair die has 1 to 6 with the same chance. If the object is biased, the simple formula may not be valid in the same direct way. Equal likelihood means each outcome has the same chance, so probability counting can be used directly only then. A fair coin is tossed once. The outcomes H and T each have chance 1/2, so they are equally likely. This is why probability of head is 1/2. Students may be asked to identify whether an experiment is fair or to decide if the outcomes are equally likely. A common wrong answer is saying outcomes are equally likely only because there are two outcomes, while fairness is actually the deciding point.
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