Question

Prove that probability of event always lies between 0 and 1​

Answer 1

1) The probability of an event which is impossible to occur is 0. Such an event is called an Impossible event.

2) The probability of an event which is sure (or certain) to occur is 1. Such an event is called a Sure event or a Certain event.

3) The probability of an event is greater than or equal to 0 and less than or equal to 1. In short, 0 ≤ P(E) ≤ 1.

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Answer 2

SOLUTION

TO PROVE

The probability of event always lies between 0 and 1

PROOF

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

Thus we have

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

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

Hence the proof follows

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