## NCERT Solutions for Class 12 Maths Chapter 13 Probability (Ex 13.3) Exercise 13.3

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1. What is conditional probability?

Conditional probability of an event is defined as the likelihood of an event or outcome which is based on the occurrence of the previous event or outcome. For example the conditional probability of an event B is based on the knowledge that an event A has already occured. This probability is usually written as P (B/A) which is read as probability of B given A. In case both the events are not independent then the probability of intersection of both the events is equal to the product of the probability of previous event and conditional probability.

P(A&B) = P(A)P(B/A).

2. What are the conditions for bernoulli trials?

Bernoulli trials are the trials of random experiment if they satisfy the following conditions:

The number of trials should be finite.

All the trials done should be independent.

Each trial must have only two outcomes. (i.e, success or failure).

The probability of success should be the same for each trial.

3. What are the topics covered in class 12 maths chapter 13?

The chapter starts with the introduction of probability where the discovery of probability is discussed. Later, we get to know what conditional probability is and what are its properties. This is followed by the multiplication theorem on probability which leads to the discussion of independent events. We learn about Bayes theorem which is divided into smaller sections like partition of sample space and theorem of total probability. The chapter ends with probability distribution of random variables, mean of random variables, variance of random variables, Bernoulli's Trials and Binomial Distribution.

4. What are the benefits of solving NCERT solutions by Vedantu?

NCERT solutions by Vedantu is prepared strictly according to the latest CBSE syllabus and it is in the most comprehensible form of the chapter containing all the important points and formulas. The subject matter experts prepared the NCERT solutions with an aim to make the learning process more convenient and fun.

5. Explain the partition of a sample space.

A given group of events (denoted by E1, E2, ..., En) is considered as representing the partition of a sample space (denoted by S) when they are disjoint pairwise, and exhaustive, while having nonzero probabilities. To understand better the partition of a sample space, it is advisable that you download the NCERT solutions by Vedantu for Class 12 Maths that are sure to help you in clearing your concepts easily. The NCERT Solutions are available on the Vedantu website and the app.

6. What is the theorem of Total Probability?

The theorem of total probability explains that when A1, A2, …… A denotes the partition of a given sample space(S) so that the probability of all the events is nonzero, in that case, the probability of the occurrence of event ‘E’ in this sample space can be obtained by summing up the probabilities of all other events in this sample space.

7. How many questions are included in Exercise 13.3 Of Class 12 Maths?

A total of 14 questions have been included in Exercise 13.3 of Class 12 Maths Chapter 13 Probability. The problems to be solved here focus majorly on providing proper knowledge of the practical application of the concepts and theorems discussed above. If you require any further help regarding solving these questions, it's a good idea to download the NCERT solutions by Vedantu for free to help you properly understand and effectively solve all the questions both in the exercise as well as the exams.

8. What are the real-time applications of Probability?

Probability refers to the study of the chance that an event will occur or not. It is used practically in several cases without knowing. All things from the toss before a game of cricket to whether we'll study at a University are checked using probability. Some common Practical applications of Probability are:

Weather forecasting

Medical Decisions

Politics

Sports and games

Choosing Insurance Policies

Flipping a Coin or Dice.

9. What are the Independent event and Bayes theorem important formulas that come in Class 12 Maths Chapter 13?

Independent events:

2 events E and F are independent, if

P(FIE) = P (F) provided P (E) = 0

OR

P (EIF) = P (E) provided P (F) = 0

OR

P(EF) = P(E). P (F)

Bayes Theorem

E₁, E₂,..., En can represent the partition of sample space S when

En E, = 0, i is not equal to j, i, j = 1, 2, 3,..., n

OR

E_{1} E_{2} E_{1}= S

OR

P(E) > 0 for all i = 1, 2, ..., n.