# NCERT Solutions for Class 12 Maths Chapter 13

NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.1, 13.2, 13.3, 13.4, 13.5 and Miscellaneous Exercises in PDF format to free download updated for new academic session 2021-2022.

## NCERT Solutions for Class 12 Maths Chapter 13

• ### CBSE NCERT Solutions for Class 12 Maths Chapter 13 in Hindi and English

 Class: 12 Mathematics Chapter 13: Probability

### Class 12 Math Exerrcise 13.1 and 13.2 in Videos

Class 12 Math Chapter 13 Exerrcise 13.1 Solution
Class 12 Math Chapter 13 Exerrcise 13.2 Solution

### Class 12 Math Exerrcise 13.3 and 13.4 in Videos

Class 12 Math Chapter 13 Exerrcise 13.3 Solution
Class 12 Math Chapter 13 Exerrcise 13.4 Solution

### Class 12 Math Exerrcise 13.5 and Miscellaneous in Videos

Class 12 Math Chapter 13 Exerrcise 13.5 Solution
Class 12 Math Chapter 13 Miscellaneous Exerrcise

### 12th Maths Chapter 13 Solutions

NCERT Solutions for Class 12 Maths Chapter 13 in PDF format free to download updated for new academic session 2021-2022. Join the discussion forum to ask your doubts in NIOS or CBSE Boards. Download Class 12 Maths Offline App or Class 12 Ganit App in Hindi Medium and NCERT Books for new session based on new CBSE Syllabus.

• ### Chapter 13 Solutions in PDF

#### Previous Year’s Questions

1. Often it is taken that a truthful person commands, more respect in the society. A man is known to speak the truth 4 out of 5 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. Do you also agree that the value of truthfulness leads to more respect in the society? [Delhi 2017]
2. Prove that if E and F are independent events, then the events E and F are also independent. [Delhi 2017]
3. A couple has 2 children. Find the probability that both are boys, if it is known that (i) one of them is a boy (ii) the older child is a boy. [CBSE Sample Paper 2017]
4. A bag contains (2n +1) coins. It is known that ‘n’ of these coins ha e a head on both its sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is 31/42, find the value of ‘n’. [CBSE Sample Paper 2017]
##### Important Questions for practice
1. Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1:2:4. The probabilities that A, B and C can introduce changes to improve profits of the company are 0.8, 0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C. [Delhi 2016]
2. A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins. [Delhi 2016]
3. An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and variance of the distribution. [Delhi 2016]
4. A problem in mathematics is given to 4 students A, B, C, D. Their chances of solving the problem, respectively, are 1/3, 1/4, 1/5 and 2/3. What is the probability that (i) the problem will be solved? (ii) at most one of them will solve the problem? [CBSE Sample Paper 2016]

###### Questions from Board Papers

1. A Bag I contains 5 red and 4 white balls and a Bag II contains 3 red and 3 white balls. Two balls are transferred from the Bag I to the Bag II and then one ball is drawn from the Bag II. If the ball drawn from the Bag II is red, then find the probability that one red ball and one white ball are transferred from the Bag I to the Bag II. [CBSE Sample Paper 2016]
2. Find the mean, the variance and the standard deviation of the number of doublets in three throws of a pair of dice. [CBSE Sample Paper 2016]
3. From a lot of 15 bulbs which include 5 defectives, a sample of 2 bulbs is drawn at random (without replacement). Find the probability distribution of the number of defective bulbs. [Delhi 2015C]

4. Probability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem. [Delhi 2015C]
5. A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and two balls are drawn at random without replacement from the bag and are found to be both red. Find the probability that the balls are drawn from the first bag. [Delhi 2015C]

### Important Questions on 12th Maths Chapter 13

##### What is conditional probability?

If E and F are two events associated with the same sample space of a random experiment, then the conditional probability of the event E under the condition that the event F has occurred, written as P (E | F).

##### What is Multiplication Theorem on Probability?

Let E and F be two events associated with a sample space of an experiment. Then P (E ∩ F) = P (E) P (F | E), P (E) ≠ 0.

##### What are independent events?

Let E and F be two events associated with a sample space S. If the probability of occurrence of one of them is not affected by the occurrence of the other, then the two events are independent.

##### What is random variable?

A random variable is a real valued function whose domain is the sample space of a random experiment.       