NCERT Solutions Class 11 Maths Chapter 14 guides you through probability concepts with clear solutions to all 38 questions across 3 exercises. You’ll learn how to calculate probabilities using classical and axiomatic approaches, understand mutually exclusive and exhaustive events, apply probability axioms, and solve problems involving sample spaces and event operations. These foundational concepts are essential for statistics, data analysis, and advanced probability theory in Class 12.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 11 Maths Chapter 14 Probability – Complete Guide
NCERT Class 11 Chapter 14 on Probability introduces you to one of the most fascinating and practical branches of mathematics. You’ll explore how probability helps us quantify uncertainty and make informed decisions in everyday life—from weather forecasting to game strategies, from medical diagnoses to financial planning. This chapter builds upon your basic understanding from Class 10 and takes you deeper into the mathematical foundations of probability theory.
📊 CBSE Class 11 Maths Chapter 14 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 6 Marks |
| Unit Name | Statistics and Probability |
| Difficulty Level | Medium |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You will learn about random experiments and their outcomes, understand how to define sample spaces and events systematically, and master the classical definition of probability. The chapter covers crucial concepts like mutually exclusive events, exhaustive events, complementary events, and the algebra of events using set operations. You’ll also be introduced to the axiomatic approach to probability, which provides a rigorous mathematical framework for all probability calculations.
For CBSE board exams, this chapter carries 6 marks and is considered of high importance with medium difficulty level. You can expect 2-3 questions including MCQs worth 1 mark, short answer questions worth 2 marks, and occasionally a long answer question worth 4 marks. The problems typically test your understanding of probability definitions, your ability to identify sample spaces correctly, and your skill in calculating probabilities of compound events.
Quick Facts – Class 11 Chapter 14
| 📖 Chapter Number | Chapter 14 |
| 📚 Chapter Name | Probability |
| ✏️ Total Exercises | 3 Exercises |
| ❓ Total Questions | 38 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering Chapter 14 is essential not only for your Class 11 exams but also as a foundation for Class 12, where you’ll study conditional probability, Bayes’ theorem, and probability distributions. With clear concepts and regular practice of NCERT solutions, you’ll find probability both interesting and scoring in your examinations.
NCERT Solutions Class 11 Maths Chapter 14 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 14.1 | Complete step-by-step solutions for 7 questions | 📥 Download PDF |
| EXERCISE 14.2 | Complete step-by-step solutions for 21 questions | 📥 Download PDF |
| Miscellaneous Exercise on Chapter 14 | Complete step-by-step solutions for 10 questions | 📥 Download PDF |
Probability – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Probability of an Event \(P(E) = \frac{\text{Number of outcomes favorable to E}}{\text{Total number of possible outcomes}}\) | Calculates the probability of event E occurring. Note: Ensure all outcomes are equally likely. P(E) always lies between 0 and 1 (inclusive). | Whenever you need to find the probability of a single event in a sample space with equally likely outcomes. |
| Probability of ‘Not E’ \(P(\text{not } E) = 1 – P(E)\) | Calculates the probability of event E *not* occurring (complement of E). Note: Also written as \(P(\overline{E})\) or \(P(E’)\). ‘Not E’ and ‘E’ are complementary events. | When it’s easier to calculate the probability of E and subtract from 1 to find the probability of ‘not E’. |
| Probability of ‘A or B’ (Inclusive) \(P(A \cup B) = P(A) + P(B) – P(A \cap B)\) | Calculates the probability of either event A or event B (or both) occurring. Note: Remember to subtract the intersection \(P(A \cap B)\) to avoid double-counting if A and B are not mutually exclusive. | When you need to find the probability of the union of two events. |
| Probability of ‘A and B’ \(P(A \cap B) = P(A) + P(B) – P(A \cup B)\) | Calculates the probability of both event A and event B occurring. Note: Rearrangement of the ‘A or B’ formula. Crucial for understanding combined probabilities. | When you need to find the probability of the intersection of two events. |
| Probability of Mutually Exclusive Events (‘A or B’) \(P(A \cup B) = P(A) + P(B)\) | Calculates the probability of either event A or event B occurring when A and B cannot happen at the same time. Note: Mutually exclusive events cannot occur simultaneously. Example: Tossing a coin and getting both heads and tails. | When events A and B are mutually exclusive (disjoint), meaning \(P(A \cap B) = 0\). |
| Probability of A or B or C \(P(A \cup B \cup C) = P(A) + P(B) + P(C) – P(A \cap B) – P(B \cap C) – P(A \cap C) + P(A \cap B \cap C)\) | Calculates the probability of A or B or C occurring. Note: A generalization of the ‘A or B’ formula. Be careful with signs and intersections. | When dealing with three events and needing to find the probability of at least one of them happening. |
| Axiomatic Approach: Sum of Probabilities \(\sum_{i=1}^{n} P(E_i) = 1\) | The sum of probabilities of all elementary events in a sample space is 1. Note: Each \(E_i\) represents a single outcome. This is a fundamental axiom of probability. | When you need to verify that a probability distribution is valid, or when you need to find a missing probability value. |
| Conditional Probability \(P(A|B) = \frac{P(A \cap B)}{P(B)}\) | Probability of event A happening given that event B has already happened. Note: P(B) must be greater than 0. \(P(A|B)\) is read as ‘probability of A given B’. | When the occurrence of one event affects the probability of another event. |
| Multiplication Rule of Probability \(P(A \cap B) = P(A) \cdot P(B|A)\) | Probability of both A and B occurring, considering the dependence between them. Note: Can also be written as \(P(A \cap B) = P(B) \cdot P(A|B)\). | When you know the probability of A and the conditional probability of B given A. |
| Independent Events \(P(A \cap B) = P(A) \cdot P(B)\) | Probability of both A and B occurring when A and B are independent (one doesn’t affect the other). Note: If A and B are independent, \(P(A|B) = P(A)\) and \(P(B|A) = P(B)\). | When events A and B are independent. |
| Total Probability Theorem \(P(A) = P(A \cap B_1) + P(A \cap B_2) + … + P(A \cap B_n)\) | The probability of an event A can be expressed as the sum of the probabilities of A occurring in conjunction with each of a set of mutually exclusive and exhaustive events \(B_i\). Note: Also expressible as \(P(A) = P(B_1)P(A|B_1) + P(B_2)P(A|B_2) + … + P(B_n)P(A|B_n)\). | When the sample space can be partitioned into several mutually exclusive events. |
Frequently Asked Questions – NCERT Class 11 Maths Chapter 14
📚 Related Study Materials – Class 11 Maths Resources
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