medium difficulty5 min

Checking validity of a probability value

A probability value is valid only if it lies between 0 and 1, including both ends.

In one line: Probability stays between zero and one.

Understand it

This rule helps students check whether an answer makes sense. A negative probability is impossible, and a value greater than 1 is also impossible. Every probability in Class 10 should satisfy 0 ≤ P(E) ≤ 1, no matter how the event is described.

Example

A probability of 5/4 is not valid because it is greater than 1.

Formula and rule

Any probability value must satisfy 0 ≤ P(E) ≤ 1.

See it worked out

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

Worked example

1If a calculation gives 9/8 for probability, it is invalid because 9/8 is greater than 1.
2The student should recheck the sample space or favourable count.

Method you can reuse

1Solve the probability expression.
2Compare the result with 0 and 1.
3If it is outside the range, it is invalid.
4Recheck the original counting.

Visual tip

A number line from 0 to 1 is a quick way to check whether an answer is possible.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A student gets -2/3 as the probability of an event. Is this value valid?

Think first, then show answer

No, it is not valid because probability cannot be negative. A valid probability must lie between 0 and 1.

Common wrong answer

A common wrong answer is saying any fraction is valid just because it came from a calculation, but probability has a fixed range.

Don't mix this up

Students sometimes accept an answer without checking whether it lies in the allowed range.

Exam tip

After solving, quickly test your answer: is it between 0 and 1? If not, recheck the counting.

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 given a calculated value and asked whether it can be a probability or not.

1
Enough for 1 mark
A probability value is valid only if it lies between 0 and 1, including both ends.
2
Add for 2 marks
Example: A probability of 5/4 is not valid because it is greater than 1.

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