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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.
 

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

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.
 

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:
 

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

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

(iii) Getting an even number
 

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

(i) Getting an odd number
 

(ii) Getting a multiple of 3
 

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.
 

(ii) Getting an even number on both dice.
 

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

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

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

(ii) Getting an odd number on the first die
 

(iii) Getting a doublet.





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