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# NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.1 Probability - PDF Download

Class 10 NCERT solutions for class 10 maths chapter 14 ex 14.1 Probability allow students to gain an in-depth understanding of theoretical probability and explain how it's different from empirical probability. Theoretical probability aims to predict the outcome of an event based on certain assumptions.

Ex 14.1 in NCERT solutions class 10 maths chapter 14 can be solved by using the theoretical probability formula. There are many examples in the ex 14.1 where you can understand the problem and solution step by step. Students will encounter new terms such as 'impossible events', 'certain' or 'certain' events, and 'equally probable' events.

The ex 14.1 consists of a series of twenty-five questions, which are derived from the above-mentioned concepts. The questions are presented in a manner that is both relatable and captivating. The PDF version of NCERT solution for ex 14.1 Probability class 10 maths is available for download on eSaral. You can also learn about it from the eSaral website.  Alternatively, you can also download the PDF for free.

## Topics Covered in Exercise 14.1 Class 10 Mathematics Questions

NCERT solutions class 10 maths chapter 14 ex 14.1 covers the concepts of probability. Here, you will get to know about the theoretical approach of probability.

 1 Probability - A Theoretical Approach
1. Probability - A Theoretical Approach - In this chapter, theoretical probability will be studied in detail. Theoretical probability is a concept that describes the probability that an event is likely to occur. During these events, only the possible outcomes will be assumed, but no experiments will be conducted. Theoretical probability is also known as classical probability.

Here is the formula to calculate theoretical probability:

P(E) = Number of outcomes favorable to E/ Number of all possible outcomes of the experiment

Events and Outcomes - Before we dive into probability, let’s first understand what events and outcomes are. An event is the outcome of an experiment. The outcome of an experiment is known as an event with possible outcomes.

We have the following types of events and outcomes:

Types of Events

There are 5 types of events - Sure events (certain), Impossible events, Normal events, Complementary events, and Elementary events.

1. Sure Event (Certain Event) - A sure event is something that's always going to happen, irrespective of the other factors. For instance, if you get a number from 1 to 6, it's always going to be 1, so the probability of that happening is always 1.

P(Sure Event) = 1

1. Impossible Event - An Impossible event is something that can't happen. For example, if you want to get a number higher than 6, the probability of that happening is 0. So, the probability of an impossible event happening are always 0.

P(Impossible Event) = 0

1. Normal Event - A normal event can be any event with a probability from 0 to 1 inclusive. It can also be a sure event or an impossible event. A normal event has a probability of 1/6 on a die.

0 <= P(E) <= 1

1. Complementary event - An event is a complementary event if the probability of occurrence is equal to the probability of non-occurrence. The probability of obtaining a number that is less than 3 on a die is 2/6, and the probability of not obtaining a number less than3 is 4/6. Therefore, the sum of these probabilities is equal to one.

P(E) + P(E’) = 1

1. Elementary event - An elementary event is an event that has only one outcome. The probability of obtaining the number two on a die is equal to 1/6. Similarly, the probability of achieving the number one on a die is equivalent to 1/6 and the same for all other numbers. The sum of the probabilities of all elementary occurrences equals 1.

P(E1) + P(E2) + P(E3) + … = 1

Types of Outcomes

There are two different types of outcomes: equal likely outcome, and non-equally likely outcome.

1. Equally Likely Outcome - An equally likely outcome is the outcome with the same outcome and probability. For Example, throwing a coin will result in an equal probability of either a head or a tail, with each of them having a probability of 1/2.

2. Non-Equally likely outcome - An outcome that is not equally likely is an outcome that is uncertain in its results and dependent on a variety of other factors. For example, if a user attempts to start a vehicle, and the vehicle either begins or fails to start, this results in a non-equally likely outcome, as the vehicle will always begin unless it requires servicing or maintenance.

## Tips for Solving Exercise 14.1 Class 10 chapter 14 Probability

Ncert solutions for class 10 maths chapter 14 ex 14.1 is based on concepts of theoretical probability. Our subject experts have compiled some of the important tips before solving the ex 14.1 questions. You can check them  below.

1. Our subject experts have compiled some of the important tips before solving the ex 14.1 questions. You can check them  below. The majority of questions in the exercise 14.1 are based on the concept of probability.

2. Students must read and comprehend the solved examples and practice them on their own. It is recommended to students to go through the concepts of the theoretical approach of probability.

3. eSaral solutions for class 10 maths chapter 14 ex 14.1 provides a number of helpful tips and tricks that will assist students in navigating the topics presented in the chapter.

## Importance of Solving Ex 14.1 Class 10 Maths chapter 14 Probability

You will get significant benefits of solving ex 14.1 class 10 maths chapter 14.

1. You'll get an in-depth understanding of the ex 14.1. it covers in a clear and straightforward way.

2. All the doubts that may arise during solving the exercise questions will be solved through the implementation of these solutions.

3. Our mathematics expert team of eSaral have provided some important tips on how to solve difficult questions of ex 14.1.

4. It encourages students to come up with different ways to solve problems.