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Type of Event - Elementry

notes

the sum of the probabilities of all the elementary events of an experiment is 1. This is true in general also.

Example  : Suppose we throw a die once. (i) What is the probability of getting a number greater than 4 ? (ii) What is the probability of getting a number less than or equal to 4 ?

Solution : (i) Here, let E be the event ‘getting a number greater than 4’. The number of possible outcomes is six : 1, 2, 3, 4, 5 and 6, and the outcomes favourable to E are 5 and 6. Therefore, the number of outcomes favourable to E is 2. So,

`P(E)=P("number greater than 4")=2/6=1/3`

(ii) Let F be the event ‘getting a number less than or equal to 4.
Number of possible outcomes = 6
Outcomes favourable to the event F are 1, 2, 3, 4.
So, the number of outcomes favourable to F is 4.

therefore `P(F)=4/6=2/3`

Are the events E and F in the example above elementary events? No, they are not because the event E has 2  outcomes and the event F has 4 outcomes.

definition

An event having only one outcome of the experiment is called an elementary event.

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