CBSE Class 10 Mathematics • Chapter 14 • Revision 2026
Probability Class 10
Understand chance with our Probability Class 10 notes and mind map PDF. The PDF contains notes and a mind map for organising your revision. Use the explanations below to learn probability formulas, count outcomes correctly and practise questions involving coins, dice, cards and coloured balls.
Probability measures how likely an event is to happen. When a fair coin is tossed, we cannot predict the individual result with certainty, but we can calculate the chance of getting a head. In Class 10 Probability, you use a clear sequence: identify the experiment, list possible outcomes, count favourable outcomes and apply the correct formula.
Most mistakes in this chapter come from counting rather than calculation. Two dice have 36 ordered outcomes, face cards do not include aces, and “at least one” has a different meaning from “exactly one”. These notes explain those distinctions with examples.
Probability Class 10 Notes: Key Definitions
- Random experiment: An experiment whose individual result cannot be predicted with certainty beforehand.
- Outcome: A possible result, such as rolling a 4.
- Sample space: The set of all possible outcomes.
- Event: A collection of outcomes satisfying a condition.
- Elementary event: An event containing one outcome.
- Equally likely outcomes: Outcomes having equal chances.
- Complementary event: The event that the original event does not occur.
The Main Probability Formula
For a finite sample space with equally likely outcomes:
P(E) = number of favourable outcomes ÷ total number of outcomes
.
Check the equally likely condition before using this counting formula. For a fair die, all six faces have equal chances. For a biased die, counting faces alone is insufficient.
Probability Class 10 Formula Sheet
| Concept | Rule | Example |
|---|---|---|
| Probability of an event | P(E) = favourable outcomes ÷ total equally likely outcomes | Even number on a fair die: 3/6 = 1/2. |
| Range | 0 ≤ P(E) ≤ 1 | Probability cannot be negative or exceed 1. |
| Impossible event | P(E) = 0 | Rolling 8 on a standard six-sided die. |
| Certain event | P(E) = 1 | Rolling a number from 1 to 6 on a standard die. |
| Complement | P(not E) = 1 − P(E) | If P(red) = 2/5, then P(not red) = 3/5. |
| All elementary outcomes | Their probabilities add to 1. | For a fair coin: 1/2 + 1/2 = 1. |
Probability Class 10 Questions with Solutions
Example 1: A Prime Number on a Die
A fair six-sided die is rolled. Find the probability of getting a prime number.
Possible outcomes: 1, 2, 3, 4, 5, 6.
Prime outcomes: 2, 3, 5.
Favourable outcomes = 3
Total outcomes = 6
Probability = 3/6
= 1/2.
Remember that 1 is not a prime number.
Example 2: Exactly One Head in Two Coin Tosses
A fair coin is tossed twice independently. Find the probability of getting exactly one head.
Sample space: HH, HT, TH, TT.
Favourable outcomes: HT, TH.
Probability = 2/4
= 1/2.
HT and TH are different outcomes because the order of the tosses is different.
Example 3: At Least One Head
For the same two independent fair-coin tosses, find the probability of getting at least one head.
Favourable outcomes: HH, HT, TH.
Probability = 3/4.
Alternatively, use the complement:
P(at least one head) = 1 − P(no heads)
= 1 − 1/4
= 3/4.
Example 4: A Sum of 7 on Two Dice
Two fair six-sided dice are rolled independently. Find the probability that their sum is 7.
Total ordered outcomes = 6 × 6
= 36
Favourable pairs:
(1,6), (2,5), (3,4), (4,3), (5,2), (6,1).
Favourable outcomes = 6
Probability = 6/36
= 1/6.
Dice Sums Are Not Equally Likely
The possible sums 2 to 12 do not each have probability 1/11. A sum of 2 has one ordered outcome, (1,1), while a sum of 7 has six. Count the 36 ordered dice pairs before calculating probabilities involving sums.
Example 5: Drawing a Face Card
One card is selected uniformly at random from a standard deck of 52 cards without jokers. Find the probability of a face card.
Face cards are jacks, queens and kings.
Number of face cards = 3 × 4
= 12
Probability = 12/52
= 3/13.
Aces are not counted as face cards.
Example 6: Selecting a Coloured Ball
A bag contains 5 red, 3 blue and 2 green balls. Each ball is equally likely to be selected. Find the probability of selecting a ball that is not blue.
Total balls = 5 + 3 + 2
= 10
Balls that are not blue = 5 + 2
= 7
Probability = 7/10.
Using the complement:
P(not blue) = 1 − 3/10
= 7/10.
Cards and Dice: Quick Revision Table
| Experiment or Group | Count | Important Detail |
|---|---|---|
| One six-sided die | 6 outcomes | Numbers 1 to 6. |
| Two six-sided dice | 36 ordered outcomes | (2,5) and (5,2) are distinct. |
| Two coin tosses | 4 ordered outcomes | HH, HT, TH, TT. |
| Standard deck without jokers | 52 cards | Four suits, each containing 13 cards. |
| Red cards | 26 | Hearts and diamonds. |
| Black cards | 26 | Clubs and spades. |
| Face cards | 12 | Four jacks, four queens and four kings. |
| Aces | 4 | One in each suit. |
How to Solve Probability Word Problems
- Identify what is tossed, rolled, drawn or selected.
- State the assumptions, such as a fair die or equally likely selection.
- List or count the complete sample space.
- Interpret the event carefully: exactly, at least, at most or not.
- Count favourable outcomes without repetition or omission.
- Divide by the total and simplify the fraction.
- Check that the answer lies between 0 and 1.
In a case-based question, several events may refer to the same experiment. Use the same sample space unless the question changes the selection process. If an object is removed before a second selection, the total number available changes.
Probability Class 10 Mind Map for Revision
Organise your Probability Class 10 mind map around random experiments, sample spaces, events, the probability formula and complements. Connect each idea to an example involving coins, dice, cards or balls.
For your 2026 revision, practise writing the sample space before looking at a solution. Then solve one direct counting question and one complement question. This builds the counting skills needed for MCQs, word problems and textbook exercises.
Continue Your Probability Practice
Use the Class 10 worksheet collection to find chapter practice resources.
Review grouped data with Statistics Class 10 notes and mind map , or explore all available chapters in the CBSE Class 10 Maths notes collection .
Frequently Asked Questions
What is probability in Class 10 Maths?
Probability is a numerical measure of an event’s likelihood. Its value lies between 0 and 1. For a finite set of equally likely outcomes, divide the favourable outcome count by the total outcome count.
Why do two dice have 36 outcomes instead of 12?
Each of the first die’s six results can occur with any of the second die’s six results. This gives 6 × 6 = 36 ordered pairs. Adding 6 + 6 does not count all possible combinations.
Are (1,6) and (6,1) different outcomes?
Yes. In (1,6), the first die shows 1 and the second shows 6. In (6,1), those results are reversed. Both count when finding the probability of a sum of 7.
What is the difference between exactly one and at least one?
Exactly one head means one head and one tail in two tosses. At least one head includes either one head or two heads. For two independent fair-coin tosses, their probabilities are 1/2 and 3/4 respectively.
When should I use the complement rule?
Use it when the opposite event is easier to count. For example, “at least one head” is the complement of “no heads”. Calculate the simpler event and subtract its probability from 1.
Are aces face cards?
No. Face cards are jacks, queens and kings. A standard 52-card deck has 12 face cards and 4 aces.
Can probability be greater than 1 or negative?
No. A probability must lie between 0 and 1 inclusive. An answer outside this range means the counts or calculation need checking.
Is the probability of every possible result automatically equal?
No. Equality depends on the experiment. Fair-die faces have equal chances, but two-dice sums do not. A spinner with unequal sectors also requires more information than simply counting its sectors.
What is the difference between theoretical and experimental probability?
Theoretical probability is calculated from a model of the experiment. Experimental probability is the observed frequency of an event divided by the number of trials. A small experiment may give a result different from the theoretical probability.
Can I add probabilities when a question says “or”?
Add them directly when the events cannot occur together. If they overlap, subtract the overlap once to avoid double counting. A king or a heart includes the king of hearts in both groups, so it must be counted only once.
What does the Probability Class 10 PDF contain?
The PDF contains notes and a mind map. Use them to revise definitions, formulas and connections between ideas, then practise questions to improve outcome counting.
How can I avoid mistakes in Probability Class 10?
Write the sample space, check whether outcomes are equally likely and read words such as “exactly” and “at least” carefully. Count ordered dice pairs separately, exclude aces from face cards and simplify the final fraction.
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