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Probability

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Probability - Lesson Summary

In a daily life come across the words like probably, likely, may be, chance and hope etc. All these are synonyms to probability.

Probability:
Probability is defined as the numerical method of measuring uncertainty involved in a situation.
It is widely used in the study of mathematics, statistics, gambling, physical science, biological science, weather forecasting, finance etc. to draw conclusions.

Experiment:
An experiment is defined as an action or process that results in well defined outcomes.

Random experiment:
An experiment, in which we know all the results, but cannot predict them, is called a random experiment.

Outcomes:
The possible results of an experiment are called the outcomes.

Event:
A combination of outcomes is called an event.

Elementary event
An outcome of a random experiment is called an elementary event.

Compound event
It is an event obtained by combining two or more elementary events associated to the random experiment.

Occurrence of an event
An event A associated to a random experiment is said to occur if any one of the elementary events associated  to the event A is an outcome.

Negation of an event
Every event A associated with a random experiment we define an event " not A"  which occurs when and only when A does not occur. The event "not A" is called the negation of event A and is denoted by A _ .

For example when an unbiased die is rolled getting an even number is an event. In this event the outcomes are {2,4,6}.
When an experiment is performed, outcomes are said to be equally likely, if each outcome has the same chance of occurring.

Probability of event E is defined as :

Probability of an event = No.of favourable outcomes Total number of outcomes .

For any event A, 0 ≤ P(A) ≤ 1.

And P(A) + P( A _ ) = 1.

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