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CraftExam
medium difficulty7 min

Equally likely outcomes

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

In one line: Same chance means equally likely.

Practice This Concept

Understand it

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.

Example

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

Formula and rule

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

See it worked out

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

Worked example

A fair coin is tossed once.

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

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer
They are called equally likely because each face has the same chance of appearing when the die is fair and thrown properly.

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.

Don't mix this up

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

Exam tip

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

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

Students may be asked to identify whether an experiment is fair or to decide if the outcomes are equally likely.
  1. 1

    Enough for 1 mark

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

  2. 2

    Add for 2 marks

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

  3. 3

    Add for 3 marks

    This idea is very important because the basic probability formula works properly only when outcomes are equally likely.

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