NCERT Class 12 Mathematics Mathematics Part-II: Chapter 7 — MATHEMATICS
This chapter of NCERT Class 12 Mathematics, Part-II, delves into the concept of Probability. Building upon previous knowledge of probability as a measure of uncertainty and the axiomatic approach, it introduces conditional probability. This concept explores how the occurrence of one event affects the probability of another. The chapter uses examples like coin tosses to illustrate how new information can reduce the sample space and alter probability calculations. It defines conditional probability, denoted as P(E|F), as the probability of event E occurring given that event F has already occurred. This foundational concept is crucial for understanding Bayes' theorem, the multiplication rule, and the independence of events, preparing students for advanced topics in probability and statistics within the CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 12 |
| Subject | Mathematics |
| Book | Mathematics Part-II |
| Chapter | Chapter 7 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 652 |
Learning outcomes
- Understand the concept of conditional probability.
- Calculate the probability of an event given that another event has occurred.
- Recognize the relationship between conditional probability and the intersection of events.
- Apply conditional probability to solve problems involving random experiments.
Vocabulary
| Word | Meaning |
|---|---|
| Probability | A measure of the likelihood that an event will occur. |
| Uncertainty | The state of being unknown or unpredictable. |
| Random experiment | An experiment whose outcome cannot be predicted with certainty. |
| Sample space | The set of all possible outcomes of a random experiment. |
| Event | A subset of the sample space. |
| Conditional probability | The probability of an event occurring given that another event has already occurred. |
| Equally likely outcomes | Outcomes that have the same probability of occurring. |
| Intersection of events | The event that both events occur. |
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Practice questions
- In the experiment of tossing three fair coins, what is the probability of getting at least two heads? Answer: 1/2
- If the first coin shows a tail in the three-coin toss experiment, what is the probability that at least two heads appear? Answer: 1/4
- Define conditional probability. Answer: Conditional probability P(E|F) is the probability of event E occurring given that event F has already occurred.
Practice MCQs
Q1. What is the sample space for tossing three fair coins?
Explanation: The sample space lists all possible outcomes when tossing three coins, where H represents heads and T represents tails.
Q2. Let E be the event 'at least two heads appear' and F be the event 'first coin shows tail' in the three-coin toss experiment. What is E ∩ F?
Explanation: E ∩ F represents the outcomes where both event E (at least two heads) and event F (first coin shows tail) occur. Only THH satisfies both conditions.
Q3. What is the probability of event E given that event F has occurred, P(E|F)?
Explanation: Given F has occurred (first coin is tail), the reduced sample space is {THH, THT, TTH, TTT}. Among these, THH is the outcome for E. So, P(E|F) = 1/4.
Q4. The axiomatic approach to probability was formulated by:
Explanation: A.N. Kolmogorov, a Russian mathematician, formulated the axiomatic approach to probability.
Frequently asked questions
What is the main focus of Chapter 13 of NCERT Class 12 Mathematics?
Chapter 13 focuses on the concept of Probability, with a significant emphasis on conditional probability and its applications.
What is conditional probability?
Conditional probability, denoted as P(E|F), is the probability of event E occurring given that event F has already occurred.
How does conditional probability affect the sample space?
When we know that event F has occurred, the sample space is reduced to the outcomes favorable to F, and we calculate the probability of E within this reduced space.
What are some key concepts that build upon conditional probability?
Conditional probability is foundational for understanding Bayes' theorem, the multiplication rule of probability, and the independence of events.
Who formulated the axiomatic approach to probability?
The axiomatic approach to probability was formulated by the Russian mathematician A.N. Kolmogorov.
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NCERT Class 12 Mathematics — Mathematics Part-II — Chapter 7 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.