# Occurrence of an Event

An event â€˜Aâ€™ associated to a random experiment is said to occur if any one of the elementary events associated to the event A is an outcome.

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**Trial:** A trial is an action which results in one or several outcomes.

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Consider the random experiment of throwing an unbiased dice. Let A denote the event "getting an even number". Elementary events associated to this event are: 2, 4, 6. Now, suppose that in a trial the outcome is 4, we say that the event A has occurred. In another trial, when the outcome be 3, then we say that the event A has not occurred.

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Let a dice be rolled and the outcome of the trial be 4. Then, we can say that each of the following events have occurred:

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(i) Getting a number greater than or equal to 2

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(ii) Getting a number less than or equal to 5

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(iii) Getting an even number

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On the basis of the same outcome, we can also say that the following events have not occurred:

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(i) Getting an odd number

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(ii) Getting a multiple of 3

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Let us now consider the random experiment of throwing a pair of dice. If (2, 6) is an outcome of a trial, we can say that each of the following events have occurred:

(i) Getting an even number on first die.

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(ii) Getting an even number on both dice.

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(iii) Getting 8 as the sum of the numbers on two dice.

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However, on the basis of the same outcome, one can also say that the following events have not occurred:

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(i) Getting a multiple of 3 on the first die

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(ii) Getting an odd number on the first die

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(iii) Getting a doublet.