NCERT Solutions Class 11 Maths Chapter 14 Probability Exercise 14.1

The NCERT Solutions for Class 11 Maths Chapter 14 Probability Exercise 14.1 solve every question of the first exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.

Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.

Exercise 14.1 is where students first learn to list every outcome of a random experiment and write events as sets. The exercise builds these core skills:

• Writing the sample space of coins, dice, cards and other random experiments.
• Expressing an event as a subset of the sample space.
• Using the algebra of events — union, intersection and complement.

Topics Covered in Probability Exercise 14.1

This exercise sets up the language of probability. A random experiment is one whose result cannot be predicted with certainty, like tossing a coin. The set of all possible outcomes is the sample space, written as S. Any subset of S is an event. Exercise 14.1 keeps the focus on writing S correctly and describing events as sets.

• Random experiments and outcomes: spotting the possible results of a single trial.
• Sample space: listing every outcome, like S = {H, T} for one coin toss.
• Events as sets: writing "an even number on a die" as the subset {2, 4, 6}.
• Types of events: simple, compound, sure, impossible, mutually exclusive and exhaustive.
• Algebra of events: forming A ∪ B, A ∩ B and the complement A′.

Important: an event is always a subset of the sample space, so you must fix S first before you can write any event. This single idea decides most questions of the exercise.

Question-wise Breakdown of Probability Exercise 14.1

The NCERT Solutions for Class 11 Maths Chapter 14 Probability Exercise 14.1 work through all 16 questions in order. The table below groups the questions by type so students can plan their practice. Full step-by-step answers are inside the PDF above.

Many questions have several parts, so the exercise gives strong practice on both writing a sample space and describing events within it.

Key Formulas and Definitions for Probability Exercise 14.1

Exercise 14.1 rests on clear definitions and a few counting rules rather than heavy formulas. Students should learn these before moving on to probability values.

Tip: for two dice the sample space has 36 ordered pairs, and for one card from a deck it has 52 outcomes. Fixing these counts now saves time in Exercise 14.2.

Common Mistakes in Probability Exercise 14.1

Students lose easy marks in Exercise 14.1 on small slips while listing outcomes. The list below covers the errors that show up most often in tests on the NCERT Solutions for Class 11 Maths Chapter 14 Probability Exercise 14.1.

• Missing outcomes in the sample space. For two coins S = {HH, HT, TH, TT}, not just {HH, HT, TT}.
• Treating (1, 2) and (2, 1) as the same outcome for two dice. Order matters, so both are listed.
• Confusing mutually exclusive with exhaustive. Exclusive means no overlap; exhaustive means they cover all of S.
• Writing an event outside the sample space. Every event must be a subset of the S you fixed first.

Practice Questions for Probability Exercise 14.1

After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 14.1.

Other Exercises of Chapter 14 Probability

Chapter 14 Probability has two exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 14.1 is done.

More Class 11 Maths Probability Resources

Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 14 Probability are linked below.

NCERT Solutions for Other Class 11 Maths Chapters

Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.

FAQs on NCERT Solutions for Class 11 Maths Chapter 14 Probability Exercise 14.1