Question

probility of an event is alway in between 0 and1. why?

Answer 1

The probability of an event will not be less than 0. 
This is because 0 is impossible (sure that something will not happen).

The probability of an event will not be more than 1. 
This is because 1 is certain that something will happen.


hope it will help u

Answer 2

$We know that probability is the ratio of no. of favourable outcomes to the no. of total outcomes. \\ \\ Let no. of favourable outcomes be \ n\ and that of total outcomes be \ t. \\ \\ \therefore\ Probability \ = \frac{n}{t} \\ \\ Let probability be \ p. \\ \\ p = \frac{n}{t}$

$We know that the no. of favourable outcomes is lesser than that of total outcomes. It won't be greater than no. of total outcomes. \\ \\ Also, both nos. of favourable and total outcomes won't be negative. \\ \\ Otherwise, the probability will be of invalid.$

$So, the no. of favourable outcomes lies between 0 and no. of total outcomes. \\ \\ 0 < n < t \\ \\ Divide them each by \ t. \\ \\ \frac{0}{t} < \frac{n}{t} < \frac{t}{t}\ \ \Longrightarrow\ \ 0 < p < 1 \\ \\ \\ \therefore\ Probability lies between 0 and 1.$

$Actually, there's no need for proof! \\ \\ The favourable outcome is lesser than or equal to the no. of total outcomes, and also it is greater than or equal to 0. So when we write probability, it'll be a proper fraction. Proper fractions are lesser than 1 and greater than 0, aren't they? \\ \\ That's all! \\ \\ \\ \#adithyasajeevan$