C
CraftExam
medium importancemedium8 min

Checking validity of a probability value

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

Practice This Concept

Learn the concept

Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Probability stays between zero and one.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

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.

Exam tip

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

Quick check

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

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

Answer writing and exam use

1-mark answer

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

2-mark answer

A probability value is valid only if it lies between 0 and 1, including both ends. Any probability value must satisfy 0 <= P(E) <= 1. A probability of 5/4 is not valid because it is greater than 1.

3-mark answer

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. Any probability value must satisfy 0 <= P(E) <= 1. If a calculation gives 9/8 for probability, it is invalid because 9/8 is greater than 1. The student should recheck the sample space or favourable count. Students may be given a calculated value and asked whether it can be a probability or not. A common wrong answer is saying any fraction is valid just because it came from a calculation, but probability has a fixed range.
MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept