Probability is the number of favourable outcomes from the total number of possible outcomes.

$$ Probability \ (P) = \frac{Favourable \ outcomes}{possible \ outcomes} $$

\(Probability \ (P) = \frac{Favourable \ outcomes}{possible \ outcomes}\)

**Example:** If a fair dice is throwing, then what is the probability of getting the number \('5' \ ?\)

**Solution:** number of favourable outcome = \(1\)

total number of possible outcomes = \(6\), then

$$ Probability \ (P) = \frac{Favourable \ outcomes}{possible \ outcomes} $$

\(Probability \ (P) = \frac{Favourable \ outcomes}{possible \ outcomes}\)

$$ Probability \ (P) = \frac{1}{6} $$

For solving the probability problems we need to know about-

**Dice:** Dice is the six faces (cube), basically used to play the games, numbered from 1 to 6.

**Coin:** Coin has two faces, Head and Tell. used for tossing in many games.

**Playing Cards:** These cards are used to play the games. Playing cards are the set of 52 cards. Some of the features of playing cards are given below-

**(1).** Total number of 52 cards, divided into four catagories and in every catagory there are 13 cards named Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.

**(2).** The colour of Heart and Diamond cards is Red, and The colour of Club and Spade cards is black.

**Experiment:** The process of rolling dice, tossing coin, etc. is known as Experiment and all the outcomes are known.

**Random Experiment:** The process of rolling dice, tossing coin, etc. but a perticular outcome is unknown then it is called Random Experiment.

**Sample Space:** This is a set of possible outcomes in an random experiment.

**Example:** Sample space for a dice = {1, 2, 3, 4, 5, 6}

**Event:** The set of favourable outcomes from the sample space is known as an event.

**Example:** Sample space for a dice = {1, 2, 3, 4, 5, 6}, and for odd number, event will be {1, 3, 5}