Introduction to Probability |

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#### In this post, " Introduction to Probability ", we will deal with following topics :

#### What is Probability ?

#### Probability Definition

#### Important Terms to know in Probability Theory

#### Probability Formula

#### Probability of an Event

#### Dice Probability

Let's get started !!

### Probability Definition or What is Probability :

A mathematical term to calculate uncertainty is called Probability.

### Important Terms to Know in Probability Theory :

**Random Experiment :**An experiment in which all possible outcomes are known to us is referred to as random experiment. For example : Dice Probability in which an unbiased dice is rolled and the possible outcomes are known to us that is there will be 6 outcomes ( 1, 2, 3, 4, 5, 6 ).

**Outcome :**The result of a random experiment is called outcome. For example : in Dice Probability, there are 6 possible outcomes ( 1, 2, 3, 4, 5, 6 ).

**Sample Space :**The set of all possible outcomes of a random experiment is known as sample space. For example : in Dice Probability, the sample space is the set ( 1, 2, 3, 4, 5, 6 ).

**Event :**The set of outcomes of a random experiment is called an event. For example : in Dice Probability, Let A denotes the event of odd numbers then A : { 1, 3, 5 }

**Trail :**The performance of a random experiment is called a trial. For example : The tossing of a coin and in Dice probability, rolling an unbiased dice is called a trial.

**Mutually Exclusive Events :**If the occurrence of any one excludes the happening of other in the same experiment then the events are termed as mutually exclusive events. For example : On tossing of a coin if head occur, then it prevents occurring of tail, in the same single experiment.

**Exhaustive Events :**All possible outcomes of an event are known as exhaustive events. For example, in Dice Probability If an unbiased dice is rolled then the exhaustive events are six { 1, 2, 3, 4, 5, 6 }.

**Equally Likely Event :**Two or more events are said to be equally likely if the chances of their happening are equal. For example : In throwing of an unbiased coin, result of Head and Tail is equally likely.

**Independent Events :**Two events are said to be independent if the happening of one event does not affect the happening of the other.

**Dependent Events :**Two events are said to be dependent if the happening of an event will affect the happening of the other event.

**Important points to know before solving questions on Playing Cards Probability :**

- Total number of playing cards are 52.
- There are 13 cards of each suit named Diamond, Hearts, Clubs and Spades.
- Out of which Hearts and diamonds are red suit cards.
- Spades and Clubs are black suit cards.
- Each Spade, Club, Diamond, Heart has 9 digit cards 2, 3, 4, 5, 6, 7, 8, 9 and 10.
- There are 4 Honors cards or face cards in each suit i.e. Spade, Club, Diamond, Heart contains 4 numbers of Honors cards or face cards : Ace, King, Queen and Jack.

### Probability Formula or Probability of an event :

#### Probability of an event = Favorable Number of Outcomes / Total Number of Outcomes.

For example : If an unbiased coin is tossed, then the probability of getting a head is 1/2 where 1 is the favorable number of outcomes whereas 2 is the total number of outcomes.

- Probability is expressed in the form of fractions.
- Probability ranges between 0 and 1.

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