# Introduction to Probability | What is Probability Definition | Probability Formula Introduction to Probability

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#### Dice Probability

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### 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.