NCERT Notes Class 11 Maths Chapter 14 Probability

The class 11 maths notes chapter 14 probability pull together every definition, event type, and probability rule that the CBSE Boards, JEE Main, JEE Advanced, and CUET actually test in 2026-27. These revision notes explain random experiments, sample space, events and their algebra, the axiomatic approach, and the addition rule in plain language, with a full formula table for quick recall.

You can download the complete Probability notes PDF above, then use the topic-by-topic summary and the formula table on this page for a fast last-minute revision.

• CBSE Boards: Probability closes Unit 5 (Statistics and Probability) and carries roughly 6 to 8 marks along with the Statistics chapter.
• JEE Main and CUET: expect 1 to 2 direct questions on the P(A ∪ B) addition rule, mutually exclusive events, and equally likely outcomes every year.
• What is covered: random experiments, sample space, event types, algebra of events, mutually exclusive and exhaustive events, and axiomatic probability.

Every entry in these Probability notes is curated by Collegedunia subject experts, according to the 2026-27 NCERT textbook, and checked against the last five years of CBSE Board and JEE Main papers.

Also Check:

• NCERT Solutions for Class 11 Maths Probability
• Class 11 Maths Probability Handwritten Notes

Topic-by-Topic Summary of the Probability Chapter for Class 11 Maths

The Probability chapter splits into five sub-topic blocks. The class 11 maths notes chapter 14 probability map each block to what the exam asks, so students know where the marks sit before they revise.

• Random experiments and sample space: listing every outcome of an experiment. Usually a 1 to 2-mark question on writing the sample space.
• Events and their types: impossible, sure, simple, and compound events. A frequent 1-mark MCQ block.
• Algebra of events: the events "A or B", "A and B", "not A", and "A but not B". Set language applied to outcomes.
• Mutually exclusive and exhaustive events: events that cannot happen together, and events that cover the whole sample space.
• Axiomatic probability and the addition rule: the P(A ∪ B) formula and equally likely outcomes. The 3 to 4-mark core of the chapter.

The rest of these notes take each block in order, so a first read from top to bottom mirrors the NCERT chapter flow.

Random Experiments and Sample Space in Class 11 Probability

A random experiment is an experiment with more than one possible result whose outcome cannot be predicted in advance. Tossing a coin or rolling a die are the standard examples. Each single result is called an outcome, and the set of all possible outcomes is the sample space, written S.

Every element of the sample space is a sample point. Two conditions must both hold for an experiment to be random:

• More than one outcome: the experiment has at least two possible results. A coin toss has two: heads and tails.
• Not predictable: you cannot say in advance which outcome will occur on a given trial.

Standard sample spaces to memorise: one coin gives S = {H, T}; one die gives S = {1, 2, 3, 4, 5, 6}; two coins give S = {HH, HT, TH, TT}. These appear again and again in exam questions, so write them without hesitation.

Types of Events Every Class 11 Student Must Know

An event is any subset E of the sample space S. The event happens when the outcome of the experiment belongs to E. The types of events are a high-frequency MCQ source, so the table below defines each with a quick example.

Two facts examiners love: the impossible event has probability 0 and the sure event has probability 1. A sample space with n sample points has exactly 2 to the power n possible events. Both are direct 1-mark questions.

Algebra of Events and Mutually Exclusive Events

Because an event is a subset of S, the set operations from the Sets chapter apply directly to events. The class 11 maths notes chapter 14 probability use this algebra to turn a word statement into a set expression before any probability is computed.

• Event "A or B" (A ∪ B): at least one of A and B occurs. This is the union of the two events.
• Event "A and B" (A ∩ B): both A and B occur together. This is the intersection.
• Event "not A" (A'): A does not occur. A' = S − A is the complementary event.
• Event "A but not B" (A ∩ B'): A occurs while B does not. Written A − B.

Two events are mutually exclusive when they cannot happen at the same time, so A ∩ B = ∅. A set of events is exhaustive when their union is the whole sample space S. Events that are both mutually exclusive and exhaustive split S into non-overlapping pieces that together cover every outcome.

All Formulas for Probability: Quick-Reference Table

The formula table below covers every rule the Probability chapter can generate. These formulas for probability are the ones students should copy onto a flashcard before the exam.

Important: the P(A ∪ B) = P(A) + P(B) − P(A ∩ B) rule is the single most-tested formula from this chapter in both CBSE Boards and CUET.

Axiomatic Approach to Probability and the Addition Rule

The axiomatic approach assigns a number P(E) to each event so that three axioms hold. This is the definition NCERT builds the whole chapter on, and the class 11 maths notes chapter 14 probability expect students to state it precisely.

• Axiom 1: P(E) ≥ 0 for every event E. A probability is never negative.
• Axiom 2: P(S) = 1. The sure event always has probability 1.
• Axiom 3: if A and B are mutually exclusive, then P(A ∪ B) = P(A) + P(B).

From these axioms every other result follows. When outcomes are equally likely, the probability of an event is P(E) = n(E) / n(S), the count of favourable outcomes divided by the total number of outcomes. For two events that may overlap, the general addition rule is P(A ∪ B) = P(A) + P(B) − P(A ∩ B), which reduces to P(A) + P(B) when the events are mutually exclusive.

Key Definitions and Theorems in the Probability Chapter

Beyond the formulas, a few named results carry marks in the reasoning-style questions. These are the definitions the Probability notes expect students to write out in full.

• Sample space: S is the set of all possible outcomes of a random experiment. Every event is a subset of S.
• Event: a subset E of S. E occurs when the observed outcome belongs to E.
• Mutually exclusive events: A ∩ B = ∅, so P(A ∩ B) = 0 and the two events share no outcome.
• Exhaustive events: events E1, E2, ..., En whose union is S, so one of them must occur.
• Complement rule: P(A') = 1 − P(A). The event and its complement always add to 1.

Remember that probability is always a number between 0 and 1. A value outside this range means an arithmetic slip somewhere in the working.

Common Mistakes Students Make in the Probability Chapter

Probability Weightage in CBSE Boards, JEE Main and CUET

Probability is a scoring chapter because the questions are short and rule-based. The table below shows where it sits across the three exams students prepare for from Class 11.

Tip: because this chapter is the base for Class 12 Probability (conditional probability and Bayes' theorem), a strong grip here pays off across the whole Class 11 and Class 12 syllabus.

How to Revise the Probability Chapter Quickly

Probability can be revised in about 90 minutes because the content is compact. Use the class 11 maths notes chapter 14 probability in the three-block plan below for a last-minute recap.

• 0 to 30 min: random experiments, sample space, and all five event types. Write the standard sample spaces from memory.
• 30 to 60 min: algebra of events, mutually exclusive and exhaustive events, and the three axioms.
• 60 to 90 min: the formula table, the addition rule, and two or three equally-likely-outcome problems.

Finish by flushing through the nine-row formula table until every rule can be written from memory.

Student Feedback on the Probability Notes

In a Collegedunia poll of 11,820 Class 11 Maths students conducted before the 2026 boards, 62% of students rated the addition rule for overlapping events as the trickiest part of the chapter, ahead of writing full sample spaces.

Other Probability Class 11 Maths Resources

Use these notes together with the linked resources below for the full Probability study set. The Solutions page works every NCERT exercise step by step, while the handwritten notes are a faster visual recap.

NCERT Notes for Class 11 Maths: All Chapters

FAQs on Probability Class 11 Maths Notes