medium difficulty4 min

Probability Scale

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

In one line: Probability never crosses 1 because 1 already means sure.

Understand it

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.

Example

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

Formula and rule

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

See it worked out

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

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 you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Can 1.25 be the probability of an event?

Think first, then show answer

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

Common wrong answer

Writing 130% as a probability.

Why it loses marks: It is greater than 100%, which is beyond certainty.

Don't mix this up

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

Exam tip

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

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 valid probabilities or arrange events by chance using fractions, decimals, or percentages.

1
Enough for 1 mark
The probability scale represents chance by numbers from 0 to 1, where 0 means impossible and 1 means certain.
2
Add for 2 marks
Example: The probability of getting heads on a fair coin is 1/2, which is 0.5 or 50%.
3
Add for 3 marks
Any valid probability lies between 0 and 1.

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