## Probability

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

- 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 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(E¯) = 1, where E¯ stands for ‘not E’. E and E¯ are 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 upper face

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

**Coin:** A coin has two faces termed as Head and Tail.
**Dice:** A dice is a small cube which 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.

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