Question

what is the range in probability of an event of a random experiment lies

Answer 1

Probability of an event lies between 0 and 1. Probability of an impossible event is 0 and probability of a sure event is 1 . Probability cannot be less than 0 and cannot be greater than 1.

Answer 2

The range of probability of an event of a random experiment is [ 0 , 1 ]

Given :

An event of a random experiment

To find :

The range of probability of the event

Solution :

Step 1 of 2 :

Define probability of an event of a random experiment

In any random experiment if the total number of elementary ( simple) events in the sample space be n ( a finite number) among which the number of elementary events favourable to an event E , connected with the experiment be m then the probability of the event E is denoted by P (E) and defined as

$\displaystyle \sf{}P(E) = \frac{m}{n}$

Step 2 of 2 :

Find range of probability of an event of a random experiment

Total number of possible outcomes = n

Total number of possible outcomes for the event E is m

So we have

$\sf{ 0 \leqslant m \leqslant n\: }$

$\implies \displaystyle \sf{ 0 \leqslant \frac{m}{n} \leqslant 1}$

$\implies \sf{0 \leqslant \: P(E) \: \leqslant 1}$

$\implies \sf{P(E) \in \: [ \: 0, 1 \: ]}$

Hence range of probability of an event of a random experiment is [ 0 , 1 ]

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