What is Probability Class 10 Maths: Definition and Key Concepts
By ConceptScroll Team · Published on 19 June 2026 · 4 min read
In Class 10 Maths, probability is the measure of how likely an event is to occur. Understanding what is probability class 10 maths is essential for solving problems related to chance and uncertainty in the NCERT syllabus.
Definition of Probability in Class 10 Maths
Probability is a branch of mathematics that deals with the likelihood of an event occurring. In Class 10 NCERT maths, probability is defined as the ratio of the number of favourable outcomes to the total number of possible outcomes, provided all outcomes are equally likely.
The formula for probability of an event $E$ is:
$$ P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}} $$
For example, when tossing a fair coin, the probability of getting heads is:
$$ P(\text{Heads}) = \frac{1}{2} $$
This simple definition forms the foundation for solving all probability problems in Class 10.
Types of Events and Their Probabilities
In probability, understanding different types of events helps in solving problems effectively:
- Certain Event: An event that is sure to happen. Probability = 1
- Impossible Event: An event that cannot happen. Probability = 0
- Favourable Event: The event we are interested in
- Unfavourable Event: Events other than the favourable one
Complementary Events
If $E$ is an event, then its complement $E'$ is the event that $E$ does not happen. The sum of probabilities of $E$ and $E'$ is always 1:
$$ P(E) + P(E') = 1 $$
This concept is useful in many Class 10 problems where calculating the complement is easier.
Want to test yourself on Probability? Try our free quiz →
Important Probability Formulas for Class 10 Students
Here are some key formulas to remember for the Probability chapter in Class 10 NCERT:
| Concept | Formula |
|---|---|
| Probability of event $E$ | $P(E) = \frac{n(E)}{n(S)}$ |
| Complement of $E$ | $P(E') = 1 - P(E)$ |
| Sum of probabilities | $P(E) + P(E') = 1$ |
Where:
- $n(E)$ = Number of favourable outcomes
- $n(S)$ = Total number of outcomes in sample space
Worked Example:
A die is rolled once. Find the probability of getting a number greater than 4.
- Favourable outcomes: 5, 6 → 2 outcomes
- Total outcomes: 6
$$ P(>4) = \frac{2}{6} = \frac{1}{3} $$
How to Calculate Probability: Step-by-Step Approach
Calculating probability in Class 10 involves a simple process:
1. Identify the sample space ($S$): List all possible outcomes. 2. Determine favourable outcomes ($E$): Outcomes that satisfy the event. 3. Count the outcomes: Find $n(S)$ and $n(E)$. 4. Apply the formula: Use $P(E) = \frac{n(E)}{n(S)}$.
Example:
A bag contains 3 red, 5 green, and 2 blue balls. Find the probability of drawing a green ball.
- Total balls = 3 + 5 + 2 = 10
- Favourable outcomes (green balls) = 5
$$ P(\text{green ball}) = \frac{5}{10} = \frac{1}{2} $$
This method ensures accuracy and clarity in solving probability questions.
Difference Between Theoretical and Experimental Probability
Understanding the difference between theoretical and experimental probability is important:
| Aspect | Theoretical Probability | Experimental Probability |
|---|---|---|
| Basis | Based on known possible outcomes | Based on actual experiments or trials |
| Calculation | $P(E) = \frac{n(E)}{n(S)}$ | $P(E) = \frac{\text{Number of times event occurs}}{\text{Total trials}}$ |
| Example | Probability of rolling a 3 on a die = $\frac{1}{6}$ | If 3 appears 20 times in 100 rolls, probability = $\frac{20}{100} = 0.2$ |
In Class 10, NCERT focuses mainly on theoretical probability but understanding both helps in practical applications.
Tips to Master Probability for Class 10 Exams
To excel in the Probability chapter of Class 10 NCERT Maths, follow these tips:
- Understand concepts, don’t just memorize.
- Practice all NCERT examples and exercises thoroughly.
- Use diagrams and tables to visualize problems.
- Solve previous year question papers for exam pattern familiarity.
- Revise formulas regularly and write them down separately.
- Attempt mock tests to improve speed and accuracy.
Consistent practice and clarity on what is probability class 10 maths will boost your confidence and performance.
Frequently asked questions
What is probability in simple terms for Class 10?
Probability is the chance of an event happening, calculated as favourable outcomes divided by total outcomes.
What is the range of probability values?
Probability values always lie between 0 and 1, where 0 means impossible and 1 means certain.
How do you find the probability of complementary events?
The probability of an event and its complement add up to 1, so $P(E') = 1 - P(E)$.
Can probability be greater than 1?
No, probability cannot be greater than 1 or less than 0; it always lies between 0 and 1.
Is probability only theoretical in Class 10?
Class 10 NCERT focuses on theoretical probability, but experimental probability is also important in real life.
Ready to ace this chapter?
Get the full Probability chapter — interactive notes, diagrams, worked solutions, polls and a free practice quiz — in the ConceptScroll app.
Study smarter with ConceptScroll
Daily NCERT-aligned reels, AI doubt solving and chapter quizzes — all free.
Start learning free