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Complete the following statementThe sum of the probabilities of all the elementary events of anexperiment is______

Question

Complete the following statement
The sum of the probabilities of all the elementary events of an
experiment is______

Answer

\(1\)
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Solution

Sum of probabilities of all the elementary events of an experiment is always \(1\).
Let a random experiment has  \(x_1,x_2,x_3...x_n\) as possible outcomes.
Now, elementary event is an event which has exactly one favourable outcome.
Now, from all possible outcomes , we can have exactly \(n\) elementary events  because total possible outcomes are \(n\).
Now, probability of any elementary event is \(\frac{1}{n}\) (i.e \(\frac{\text{favourable}}{\text{total}}\))
Therefore, sum of all elementary events is \(\frac{1}{n}+\frac{1}{n}+\frac{1}{n}+..+\frac{1}{n}\)
\(=\frac{n}{n}=1\) [\(\because 1+1+1...upto \ n \ times =n\)]
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