# RD Sharma Class 11 Chapter 33 Solutions (Probability)

RD Sharma Solutions for Class 11 Maths Chapter 33 – Probability will help you revise the two

approaches for probability, statistical approach and classical approach. Probability is a field in itself that treats both the approaches (classical and statistical) differently to get the best and eliminating the shortcomings of both.

In RD Sharma Solutions for Class 11 Chapter 33, you will get to know two terms, elementary events also known as outcomes and sample spaces. There are 4 exercises in the chapter with around 100 questions. There are plenty of examples where new events can be established by combining more events which are connected with a random experiment. The chapter also provides an insight into various types of events like sure events or impossible events etc.

To understand probability, we have to understand some other things like, random experiments, elementary events etc which we will be understanding as we proceed to our exercises. The word experiment means any trial done to test a hypothesis that can give some desired outcomes. There are two types of experiments, deterministic and random or probability experiments. You can learn all of these from our RD Sharma Solutions for class 11 chapter 33.

## Topics covered in RD Sharma Solutions for Class 11 Chapter 33 – Probability

Probability is one of the most important concepts as it is not just a chapter, but a whole field of mathematics and to understand it, we have to understand its concepts as well because those concepts will be used in higher classes as well.

The first thing that we will learn about is random experiments, any experiments of which the results are not fixed, meaning we don’t know what the outcome of those experiments is going to be. The results will also be more than 1. After this comes the outcomes, in the language of probability, any results coming out of random experiments are called outcomes.

For example, if we toss two coins, then there can be three possible outcomes TT, HT, TH or HH; where H heads and T is tails. And if you put outcomes in a curly bracket, then it becomes a sample space. For examples S={TT, HT, TH, HH}. Any subsets created from sets are called events, considering the above example, we can know that there are 4 subsets thus 4 events are possible. This is also an example of a sure event.

The other kind of events is simple events, compound events and impossible events. We will also be understanding about the algebra of events like complimentary events, events e or f, events e and f, mutually exclusive events and exhaustive events.

Let’s take another example if we draw 7 cards out of a well-shuffled deck of cards, what is the probability that it will get all jacks, 3 jacks or at least 3 jacks.

Here we will apply the combination, therefore the group will be n(S)= 52c7.

Now, the first is to find if all are jacks, which we will denote by A.

Therefore n(A)=4c4 X 48c3 and the probability P(A)=n(A)/n(S)

To find the probability of 3 jacks, n(B)= 4c3 X 48c4 and probability of this will be P(B)=n(B)/n(S)

To find the probability of at least 3 jacks, we have to find the probability of 3 jacks and the probability of getting 4 jacks. As we have already found out above, we can write it as,

P(At least 3 cards)= 4c3 X 48c4 / 52c7 + 4c4 X 48c3 / 52c7

Sometimes, we might be asked some questions like to find the probability of an event that will not happen. Let’s say if the event that is likely to happen is called A then to find a probability of A not happening will be called P(A’) and would be found out using 1-P(A) since we know that all the probabilities sum up to 1. We can also be asked to find the probability of one of the two events, like if we are asked to find the probability of A or B, then we denote it by P(A)=P(A∪B).

Here, we will find the probability of A and then the probability of B and then subtract it by P(A∩B). P(A∩B) is the probability of both A and B happening, which are common elements and most favourable. We can also be asked to find out the probability of one event happening, but not the other one, it can be denoted by P(A∩B’) or neither one of the event, P(A∪B)’.

### Discussion on the Exercises of RD Sharma Solutions for Class 11 Chapter 33 Probability

- The concept of probability has extensively been covered in 4 exercises which you can practice and ace your exams with the help of Instasolv.
- The first exercise covers the topic of sample space and elementary events and has 24 questions.
- The exercise 33.2 has 9 questions related to outcomes and if there are any special events like exclusive or exhaustive etc.
- The third exercise has 44 questions covering a wide variety of topics of combination questions to favourable events to required probability.
- The fourth exercise has 26 questions, where questions to find the probability of an event happening or not happening is asked.

### Benefits of RD Sharma Solutions for Class 11 chapter 33 – Probability by Instasolv

By the efforts of a hardworking team at Instasolv it is very easy to understand the concept of probability. Even though the subject is very deep but we have tried to provide you with all the explanations related to the chapter at one place. Instasolv makes it a point that you understand all the fundamentals of probability through RD Sharma Class 11 Maths Solutions for Chapter 33.