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## NCERT Solutions for Class 10 Maths Chapter 15

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### Class 10 Maths Solutions – Probability

#### English Medium

**Exercise 15.1****Exercise 15.2****Study Online****NCERT Books in Hindi Medium & English Medium****प्रश्नावली 15.1**

#### Previous Years Questions

##### One mark questions

- 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

- 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

- 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.

#### Term related to Probability

**Random Experiment**: A random experiment is one in which the exact outcome cannot be predicted.**Trial**: Performing a random experiment is called a trial.**Outcomes**: The result of a random experiment is called an outcome.**Sample space**: The collection of all possible outcomes of a random experiment is called a sample space.**Even**t: Any possible outcome or combination of outcomes of a random experiment is called an event.**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.**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).

**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.
- 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.