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Probability Scale

The probability scale represents chance by numbers from 0 to 1, where 0 means impossible and 1 means certain.

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Student-friendly explanation

Any valid probability lies between 0 and 1. It may be written as a fraction, decimal, or percentage, such as 1/2, 0.5, or 50%. Larger probability means greater chance.

How to write this in exams

  1. 1

    Start with the exact idea

    The probability scale represents chance by numbers from 0 to 1, where 0 means impossible and 1 means certain.

  2. 2

    Then show how to use it

    Convert forms if needed, compare their values, and reject any probability below 0 or above 1.

  3. 3

    Add one concrete example

    The probability of getting heads on a fair coin is 1/2, which is 0.5 or 50%.

  4. 4

    Avoid this incomplete answer

    Writing 130% as a probability is wrong because it is greater than 100%, which is beyond certainty.

Definition

The probability scale represents chance by numbers from 0 to 1, where 0 means impossible and 1 means certain.

Example

The probability of getting heads on a fair coin is 1/2, which is 0.5 or 50%.

Rule to remember

0 <= P(E) <= 1; 0 means impossible and 1 means certain.

Memory hook

Probability never crosses 1 because 1 already means sure.

Examples and method

Worked example

If 3 out of 10 outcomes are favourable, probability is 3/10 = 0.3 = 30%, which lies on the scale between 0 and 1.

Method to apply

Convert forms if needed, compare their values, and reject any probability below 0 or above 1.

Diagram support

Use a number line marked 0, 1/2, and 1 to compare impossible, even chance, and certain events.

How CBSE asks it

Students may be asked to identify valid probabilities or arrange events by chance using fractions, decimals, or percentages.

Avoid common mistakes

Common confusion

Students sometimes write probabilities greater than 1, such as 6/4, after counting incorrectly.

Common wrong answer

Writing 130% as a probability is wrong because it is greater than 100%, which is beyond certainty.

Exam tip

After calculating, check whether your answer lies between 0 and 1. If not, the counting is wrong.

Quick check

Can 1.25 be the probability of an event?

No, 1.25 cannot be the probability of an event because probability must lie from 0 to 1, including 0 and 1.

Answer writing and exam use

1-mark answer

The probability scale represents chance by numbers from 0 to 1, where 0 means impossible and 1 means certain.

2-mark answer

The probability scale represents chance by numbers from 0 to 1, where 0 means impossible and 1 means certain. 0 <= P(E) <= 1; 0 means impossible and 1 means certain. The probability of getting heads on a fair coin is 1/2, which is 0.5 or 50%.

3-mark answer

Any valid probability lies between 0 and 1. It may be written as a fraction, decimal, or percentage, such as 1/2, 0.5, or 50%. Larger probability means greater chance. 0 <= P(E) <= 1; 0 means impossible and 1 means certain. If 3 out of 10 outcomes are favourable, probability is 3/10 = 0.3 = 30%, which lies on the scale between 0 and 1. Students may be asked to identify valid probabilities or arrange events by chance using fractions, decimals, or percentages. Writing 130% as a probability is wrong because it is greater than 100%, which is beyond certainty.
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