NCERT Solutions for Class 10 Maths Chapter 15: Probability

Class 10 Maths Chapter 15, titled “Probability”, focuses on introducing the concept of probability and how to calculate it for different events. Probability plays a key role in understanding uncertain events and outcomes. This chapter involves theoretical approaches and practical examples.

Table of Contents

Topics and Subtopics in Chapter 15: Probability

Section Name	Topic Name
15	Probability
15.1	Introduction to Probability
15.2	A Theoretical Approach
15.3	Summary

NCERT Solutions for All Exercises in Chapter 15:

Exercise 15.1 – Introduction to Probability (20 Questions)

In this exercise, you are introduced to the basic concept of probability and how it is calculated. The formula for probability is: P(E)=Number of favorable outcomesTotal number of possible outcomesP(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

Some sample problems:

Finding the probability of a head or tail when tossing a coin.
Finding the probability of getting a certain number when rolling a die.

Exercise 15.2 – A Theoretical Approach (15 Questions)

This exercise explores theoretical probability and how to calculate it for events involving multiple steps. It also includes problems where outcomes are based on more complex scenarios such as drawing cards, multiple dice rolls, or combinations.

Key concepts covered:

Finding probability for different events using favorable and total outcomes.
Working with combined events (like drawing two cards and calculating the probability).

Exercise 15.3 – Additional Probability Problems (10 Questions)

This exercise includes a set of problems that test your understanding of the probability concepts discussed in earlier exercises. The questions involve various events, such as drawing cards from a deck, probability of different outcomes in random experiments, and others.

Sample Problem from Each Exercise:

Exercise 15.1 Example:

Q1: A die is rolled. What is the probability of getting a number less than 4?

Solution:

The total number of outcomes is 6 (numbers 1, 2, 3, 4, 5, 6).
The favorable outcomes (numbers less than 4) are 1, 2, 3.

Thus, the probability is: P(less than 4)=36=12P(\text{less than 4}) = \frac{3}{6} = \frac{1}{2}

Exercise 15.2 Example:

Q1: A card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a red card?

Solution:

A deck has 26 red cards (13 hearts and 13 diamonds).
The total number of possible outcomes is 52.

Thus, the probability is: P(red card)=2652=12P(\text{red card}) = \frac{26}{52} = \frac{1}{2}

Exercise 15.3 Example:

Q1: Two dice are rolled. What is the probability that the sum of the numbers on the two dice is 7?

Solution:

The total number of possible outcomes when two dice are rolled is 6×6=366 \times 6 = 36.
The favorable outcomes (where the sum is 7) are: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).

Thus, the probability is: P(sum of 7)=636=16P(\text{sum of 7}) = \frac{6}{36} = \frac{1}{6}

Download Solutions for All Exercises:

For detailed step-by-step solutions to all the exercises in Chapter 15: Probability, you can download the PDF of NCERT Solutions.

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