# NCERT Solutions for Class 10 Maths Chapter 15

NCERT Solutions for Class 10 Maths Chapter 15 Probability Exercise 15.1 and Exercise 15.2 in English and Hindi medium for CBSE, UP Board, MP Board free to download updated for new academic session 2021-22. These NCERT Solutions are applicable for UP Board also as UP Board has implemented NCERT Textbooks as UP Board Textbooks for the academic session 2021-2022. UP board Students can download UP Board solutions for Class 10 Maths Chapter 15 all exercises. These solutions are applicable for all the students who are following CBSE Board for academic session 2021-22. Not only NCERT Solutions but the NCERT Books also for all subjects along with Offline Apps of NCERT Textbook’s Solutions for class 10 all subjects.

Videos related to Ex 15.1 and Ex. 15.2 of class 10 Maths are given below explaining each and every questions. Explanation is in simple language, so that students can understand easily.## NCERT Solutions for Class 10 Maths Chapter 15

### 10th Maths Chapter 15 Exercise 15.1

### 10th Maths Chapter 15 Exercise 15.2

Class: 10 | Maths (English and Hindi Medium) |

Chapter 15: | Probability |

#### Class 10 Maths Exercise 15.1 Solution in Videos

### 10th Maths Chapter 15 Solutions

NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 and Exercise 15.2 of Probability is given below for academic session 2021-22. NCERT Solutions for class 10 is updated according to CBSE Curriculum 2021-2022. Join the discussion forum to ask your questions and answer the questions already asked by other users.

#### Class 10 Maths Exercise 15.2 Solution in Videos

##### What do you understand by Random Experiment?

Random Experiment: A random experiment is one in which the exact outcome cannot be predicted.

##### What is meant by Trial in Probability?

Trial: Performing a random experiment is called a trial.

##### What is meant by Outcomes?

Outcomes: The result of a random experiment is called an outcome.

##### What is Sample space in terms of Probability?

Sample space: The collection of all possible outcomes of a random experiment is called a sample space.

##### What are Events in Probability?

Event: Any possible outcome or combination of outcomes of a random experiment is called an event.

##### Which events are called Equally likely events?

Equally likely events: Two or more events of a random experiment are said to be equally likely events if each one of them have an equal chance of occurrence.

##### What is meant by Probability of an event?

Probability of an event: The chance of occurrence of the event expressed quantitatively is known as the probability of an event and denoted by P(E).

#### Previous Years Questions

ONE MARK QUESTIONS

1. A number is chosen at random from the numbers -3, -2,-1, 0, 1, 2, 3. What will be the probability that square of this number is less than or equal to 1? [CBSE 2017]

THREE MARKS QUESTIONS

1. Two different dice are thrown together. Find the probability that the numbers obtained

(i) have a sum less than7

(ii) have a product less than 16

(iii) is a doublet of odd numbers. [CBSE 2017]

FOUR MARKS QUESTIONS

1. Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25? [CBSE 2017]

##### About Probability

The measure of certainty of events in numerical values, under certain conditions, is provided by the branch of mathematics called ‘Theory of Probability. This theory has extensive use as one of the basic tools in statistics and wide range of applications in Science, engineering, biological science, medical, commerce, weather forecasting etc.

###### Historical facts!

- The concept of probability was developed in a very strange manner. In 1654, a gambler by name Chevalier de Mere approached the well-known 17th century French philosopher and mathematician Blaise Pascal regarding certain dice problems. Pascal discussed them with another French mathematician Pierre de Fermat and they found solution to dice problems. This work was the beginning of probability theory.
- Probability theory has its actual origin in the 16th century when an Italian physician and mathematician J. Cardan wrote the first book on the subject ‘The book on Games of Chance’. Since its inception, the study of Statistics and probability has attracted the attention of great mathematicians (James Bernoulli (1654 – 1705), A. de Moivre (1667 – 1754) and Pierre Simon Laplace (1749 – 1827)).
- In 1812, Pierre Simon Laplace or Pierre de Laplace (1749 – 1827, France) proposed a mathematical system of inductive reasoning based on probability. He introduced many principles of probability, one among them is, “Probability is the ratio of the favoured events to the total possible events”.
- Statistician Karl Pearson (1857 – 1936) had tossed the coin 24000 times and he got 12012 heads. Then calculated experimental probability 12012/2400 = 0.5005.

5. In the eighteenth century French De Buffon tossed a coin 4040 times and got 2048 heads. Then he calculated experimental probability 2048/4040 = 0.507.

### Important Questions on Class 10 Maths Chapter 15

##### Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

When we toss a coin, the possible outcomes are only two, head or tail, which are equally likely outcomes. Therefore, the result of an individual toss is completely unpredictable.

##### It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

Probability that two students are not having same birthday P (not E) = 0.992 Probability that two students are having same birthday P (E) = 1 − P (not E) = 1 − 0.992 = 0.008

##### A die is thrown once. Find the probability of getting a prime number.

The possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6} Number of possible outcomes of a dice = 6 Prime numbers on a dice are 2, 3, and 5. Total prime numbers on a dice = 3 Probability of getting a prime number = 3/6 =1/2

##### Five cards−−the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. What is the probability that the card is the queen?

Total number of cards = 5 Total number of queens = 1 P(getting a queen) = (Number of favourable outcomes)/(Number of total possible outcomes) =1/5

##### A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

Total number of bulbs = 20 Total number of defective bulbs = 4 P(getting a defective bulb) = (Number of favourable outcomes)/(Number of total possible outcomes) = 4/20 = 1/5

##### A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

Total number of discs = 90 Total number of two-digit numbers between 1 and 90 = 81 P (getting a two-digit number) = 91/90 = 9/10

##### How many examples are there in chapter 15 Probability of class 10 Maths?

There are two exercises in chapter 15, Probability (class 10 Maths). In the first exercise (exercise 15.1), there are 25 questions, and in the second exercise (exercise 15.2), there are five questions. So there are 30 questions in chapter 15. There are 13 examples in chapter 15 of class 10 math. All the examples and questions of this chapter are good.

##### What are real-life applications of Probability in Class 10 Maths Chapter 15?

Probability has something to do with a chance. It is the study of things that might happen or might not. We use it most of the time, usually without thinking of it.

Some real-life applications of Probability:

- Weather Forecasting: Before planning for an outing or a picnic, we always check the weather forecast.
- Flipping a coin or Dice.
- Lottery Tickets: Winning or losing a lottery is one of the most interesting examples of Probability.
- Playing Cards: There is a probability of getting a desired card when we randomly pick one out of 52.

##### Is there any optional exercise in chapter 15 of class 10th Maths?

Yes, there is an optional exercise in chapter 15 of class 10th Maths. The second exercise (exercise 15.2) is the optional exercise of chapter 15 and is not an easy exercise. Students find this exercise a little complex as compared to exercise 15.1.

##### Is chapter 15 of class 10th math easy to understand?

Chapter 15 of class 10th Maths is not easy and not difficult. It lies in the middle of easy and difficult because some examples and questions of this chapter are easy, and some are difficult. However, the difficulty level of anything varies from student to student. So, Chapter 15 of class 10th Maths is easy or not depends on students also. Some students find it difficult, some find it easy, and some find it in the middle of easy and difficult.