NCERT Book Class 10 Maths Chapter 14 Probability PDF

Ans. Chapter 14 of the Class 10 Maths NCERT Book covers the theoretical (classical) definition of probability. It introduces the sample space (the set of all possible outcomes), elementary events (individual outcomes), and the classical probability formula: P(E) = number of favourable outcomes divided by the total number of equally likely outcomes. The chapter also covers complementary events (P(E) + P(E') = 1), impossible events (P = 0), and sure events (P = 1). The exercises use everyday experiments like tossing one or two coins, rolling a die, drawing a card from a standard 52-card deck, and picking coloured marbles from a bag. The chapter has one main exercise (Exercise 14.1) with 25 questions covering the full range of probability question types tested in the 2026-27 CBSE Class 10 board exam.

Ans. The classical probability formula given in NCERT Chapter 14 is: P(E) = (Number of outcomes favourable to E) divided by (Total number of equally likely outcomes in the sample space). This formula applies only when all outcomes are equally likely (for example, a fair coin or an unbiased die). P(E) always lies between 0 and 1. A value of 0 means the event is impossible (no favourable outcomes). A value of 1 means the event is certain (every outcome is favourable). For the complementary event E', P(E') = 1 - P(E), which is a useful shortcut in questions where it is easier to count the outcomes where E does not happen than the ones where it does.

Ans. A sample space is the set of all possible outcomes of an experiment. For a single coin toss, the sample space is {H, T}. For two coins, it is {HH, HT, TH, TT}. For one die, it is {1, 2, 3, 4, 5, 6}. For drawing one card from a 52-card deck, the sample space has 52 elements. The NCERT chapter always requires students to identify the sample space before applying the probability formula, because the total number of outcomes in the sample space is the denominator of the probability fraction. Listing the sample space completely and systematically is one of the key skills practised in the solved examples and Exercise 14.1.

Ans. Complementary events are a pair of events where one event happens if and only if the other does not. For an event E, its complement E' (or E-bar) consists of all outcomes in the sample space that are not in E. The key property is P(E) + P(E') = 1, which means P(E') = 1 minus P(E). For example, if the probability of drawing a king from a deck is 4/52 = 1/13, then the probability of not drawing a king is 1 minus 1/13 = 12/13. This relationship is especially useful in board questions that ask for "at least one" or "not" type events, where the complement is simpler to calculate than the event itself.

Ans. Class 10 Maths Chapter 14 Probability has one main exercise, Exercise 14.1, which contains 25 questions. The questions cover all the probability concepts taught in the chapter: listing sample spaces, finding probability using the classical formula, using the complement rule, and applying probability to real-world contexts (cards, dice, coins, marbles). There are also several solved examples before Exercise 14.1 that model the layout and working that the CBSE board expects in the answer sheet. Students who work through all 25 questions in Exercise 14.1 and study the solved examples will be well prepared for the probability questions in the CBSE Class 10 Maths board exam.

Ans. An impossible event has no favourable outcomes in the sample space, so its probability is 0. For example, the event of rolling a 7 on a standard six-faced die is impossible because 7 is not in the sample space {1, 2, 3, 4, 5, 6}. A sure event (also called a certain event) has all outcomes in the sample space as favourable, so its probability is 1. For example, the event of rolling a number less than 7 on a standard die is a sure event. Every other event has a probability strictly between 0 and 1. The NCERT chapter uses these two extremes to confirm the range rule: 0 is less than or equal to P(E), which is less than or equal to 1.

Ans. Yes. The official NCERT Book PDF for Class 10 Maths Chapter 14 Probability is free to read and download on this page for the 2026-27 session. It is the complete chapter exactly as printed in the CBSE textbook, including all the solved examples and Exercise 14.1 with all 25 questions. You can pair the book PDF with the NCERT Solutions and revision notes for the same chapter, both linked on this page, so you can read, practise, and revise from one place without needing to search multiple sites.