CBSE Class 10 Maths Notes Chapter 15 Probability Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 15 Probability. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

## CBSE Class 10 Maths Notes Chapter 15 Probability

**Probability:** It is the numerical measurement of the degree of certainty.

- The theoretical probability associated with an event E is defined as “If there are ‘n’ elementary events associated with a random experiment and m of these are favourable to the event E then the probability of occurrence of an event is defined by P(E) as the ratio \(\frac { m }{ n }\) “.

- If P(E) = 1, then it is called a ‘Certain Event’.
- If P(E) = 0, then it is called an ‘Impossible Event’.
- The probability of an event E is a number P(E) such that: 0 ≤ P(E) ≤ 1
- An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
- For any event E, P(E) + P(\(\bar { E }\)) = 1, where \(\bar { E }\) stands for ‘not E’. E and \(\bar { E }\) is called complementary events.
- Favourable outcomes are those outcomes in the sample space that are favourable to the occurrence of an event.

**Sample Space**

A collection of all possible outcomes of an experiment is known as sample space. It is denoted by ‘S’ and represented in curly brackets.

**Examples of Sample Spaces:**

A coin is tossed = Event

E_{1} = Getting a head (H) on the upper face

E_{2} = Getting a tail (T) on the upper face

S = {H, T}

Total number of outcomes = 2

Two coins are tossed = Event = E

E_{1} = Getting a head on coin 1 and a tail on coin 2 = (H, T)

E_{2} = Getting a head on both coin 1 and coin 2 = (H, H)

E_{3} = Getting a tail on coin 1 and a head on coin 2 = (T, H)

E_{4} = Getting a tail on both, coin 1 and coin 2 = (T, T)

S = {(H, T), (H, H), (T, H), (T, T)}.

Total number of outcomes = 4

**NOTE:** In probability the order in which events occur is important

E_{1} & E_{3} are treated as different outcomes.

Important Tips

**Coin:**A coin has two faces termed a Head and Tail.**Dice:**A dice is a small cube that has between one to six spots or numbers on its sides, which is used in games.**Cards:**A pack of playing cards consists of four suits called Hearts, Spades, Diamonds, and Clubs. Each suite consists of 13 cards.

### NCERT Notes for Class 10 Maths

- Chapter 1 Real Numbers Class 10 Notes
- Chapter 2 Polynomials Class 10 Notes
- Chapter 3 Pair of Linear equations in Two Variables Class 10 Notes
- Chapter 4 Quadratic Equations Class 10 Notes
- Chapter 5 Arithmetic Progressions Class 10 Notes
- Chapter 6 Triangles Class 10 Notes
- Chapter 7 Coordinate Geometry Class 10 Notes
- Chapter 8 Introduction to Trigonometry Class 10 Notes
- Chapter 9 Some Applications of Trigonometry Class 10 Notes
- Chapter 10 Circles Class 10 Notes
- Chapter 11 Constructions Class 10 Notes
- Chapter 12 Areas related to Circles Class 10 Notes
- Chapter 13 Surface Areas and Volumes Class 10 Notes
- Chapter 14 Statistics Class 10 Notes
- Chapter 15 Probability Class 10 Notes

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