NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.1 Probability - PDF Download

NCERT solutions for class 11 maths chapter 14 exercise 14.1 Probability is dedicated to the  events such as occurrence of an event, type of events, algebra of events etc. Ex 14.1 shows us how to deal with various events. It begins with questions that ask us to determine if an event is possible or not. This theory is based on the idea that there are certain events that are sure and certain events that are impossible, and then there is an event whose probability is between 0 and 1.

There is an excessive emphasis on events that are mutually exclusive, events that have nothing in common, and thus only one event can happen at a time. In order to answer the questions in this exercise, we need to identify events that are mutually exclusive or even to define events that are mutually exclusive for an experiment. In addition, there are also questions about mutually exclusive but exhaustive events where you need to define or identify these events.

Ex 14.1 class 11 maths chapter 14 consists of a total of 7 questions that is about applying the fundamental concepts of events that the probability theory is based on. Class 11 maths chapter 14 exercise 14.1 NCERT solutions are prepared by the academic team of mathematics at eSaral. All the topics included in ex 14.1 are explained in a proper way with step by step to help you score well in examinations. These solutions are also available in PDF format to make your learning easy. Download the free PDF of NCERT solutions from the link given below.

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Topics Covered in Exercise 14.1 Class 11 Mathematics Questions

Ex 14.1 class 11 maths ch 14 is based on important topics like event, occurrence of an event, types of events, algebra of events, mutually exclusive events and exhaustive events. You can find a detailed explanation of these topics provided by the expert faculty of eSaral.

1. Event - Any subset E of a sample space S is called an event. An event is a collection of favourable outcomes.

• Occurrence of an event - The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. If the outcome ω is such that ω ∉ E, we say that the event E has not occurred.
• Types of events - Events can be divided into different categories based on the elements they contain.

1. Impossible and Sure Events - The empty set φ and the sample space S describeevents. In fact φ is called an impossible event and S, i.e., the whole sample space is called the sure event.

2. Simple Event -  If an event E has only one sample point of a sample space, it is called a simple (or elementary) event. In a sample space containing n distinct elements, there are exactly n simple events. 

3. Compound Event - If an event has more than one sample point, it is called a Compound event.

• Algebra of events - The Chapter on Sets provides an overview of the various ways in which two or more sets can be combined, such as in the form of a viz, a union, an intersection, a difference, a complement of a set, etc. Similarly, two or more events can be combined using analogous set notations. 

1. Complementary Event - For every event A, there corresponds another event A′ called the complementary event to A. It is also called the event ‘not A’. 

2. The Event ‘A or B’ - It is important to note that the combination of two sets, A and B, as defined by AB, contains all the elements that are either in A or B, or both.

When two events, A and B, are associated with a sampling space, then AB is the event either A or B, or both. This event ‘A∪B’ is also called ‘A or B’.

Therefore Event ‘A or B’ = A ∪ B

3. The Event ‘A and B’ - An intersection between two sets AB is defined as the set of the elements which are common to both sets A and B i.e., which belong to both ‘A and B’. 

If there are two events A and B, then set A B represents the event "A" and "B". 

Thus, A ∩ B = {ω : ω ∈ A and ω ∈ B}

4. The Event ‘A but not B’ - Basically, we know that A is the set of all the elements that are inside A but not inside B, so the set A-B can represent the event 'A but not B'. 

We know that  A – B = A ∩ B´

• Mutually exclusive events - In general, two events A and B are called mutually exclusive events if the occurrence of any one of them excludes the occurrence of the other event, i.e., if they can not occur simultaneously. In this case the sets A and B are disjoint.

A ∩ B =$\phi$ , i.e. A and B are disjoint sets.

Simple events of a sample space are always mutually exclusive.

• Exhaustive events - Events E₁ , E₂ ,..., En are mutually exclusive and exhaustive if E₁ ∪ E₂ ∪ ...∪ E_n = S  and E_i ∩ E_j = φ V_i ≠ j 

Tips for Solving Exercise 14.1 Class 11 Chapter 14 Probability

Our subject experts of eSaral have provided some useful tips and tricks to solve questions of ex 14.1 class 11 maths chapter 14.

1. Ex 14.1 of NCERT solutions class 11 maths chapter 14 focuses on the concept of probability and the definition of various types of events. Students need to be careful while studying these concepts.
2. The key to comprehending the questions asked in this exercise is the concept of events that are mutually exclusive and exhaustive, as opposed to events that are not mutually exclusive.
3. NCERT solutions class 11 maths chapter 14 ex 14.1 consists of questions that explain the experiment and then ask us to define the events, or where the events are specified, the students have to define the event type.
   

Importance of Solving Ex 14.1 Class 11 Maths Chapter 14 Probability

Ex 14.1 class 11 maths ch 14 combined questions which requires extra attention to solve. Here, our subject experts have provided numerous benefits of solving ex 14.1 class 11 maths chapter 14 probability. 

1. NCERT solutions class 11 maths chapter 14 ex 14.1 has significant topics and concepts related to events which are explained in easy to understand language.
2. Ex 14.1 class 11 maths chapter 14 NCERT solutions have included examples as well as important questions that are solved in stepwise manner. This will help you to solve questions with ease in exams.
3. NCERT solutions PDF will help you to cross check your answers that will boost your self-confidence.
4. By practicing questions and revising concepts from NCERT solutions class 11 maths chapter 14 ex 14.1 will improve your problem solving skills.

Frequently Asked Questions 

Question 1. What is the probability of an impossible event ?

Answer 1. There is zero probability of an impossible event.

Question 2. What do you mean by occurrence of an event?

Answer 2. The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. If the outcome ω is such that ω ∉ E, we say that the event E has not occurred.