Question

If E is any event of a random experiment then the probability of the event E belongs to *​

Answer 1

Explanation:

Definition : A random experiment is an experiment or a process for which the outcome cannot be predicted with certainty. Definition : The sample space (denoted S) of a random experiment is the set of all possible outcomes.

Answer 2

SOLUTION

GIVEN

E is any event of a random experiment

TO DETERMINE

The probability of the event E belongs to

EVALUATION

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

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

Now the total number of possible outcomes = n and the total number of possible outcomes for the event E is m

So

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

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

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

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

FINAL ANSWER

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

ADDITIONAL INFORMATION

For an impossible event, the number of favourable cases is zero and hence it's probability is 0

On the other hand for a certain event S all cases are favourable cases and hence it's probability is 1

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