# Properties of Probability

Probability has many interesting properties.

### Certain Event

An event which is sure to occur is called a sure or certain event. Probability of a sure event is taken as 1.

### Impossible Event

An event which is impossible to occur is called an impossible event. Probability of an impossible event is taken as 0.

### Range of P(E)

P(E) cannot be greater than 1, since numerator being the number of outcomes favourable to E cannot be greater than the denominator (number of all possible outcomes). Both the numerator and denominator are natural numbers, so P(E) cannot be negative. So, P(E) takes any value from 0 to 1.

0 ≤ P(E) ≤ 1

### Elementary Events

The sum of the probabilities of all the elementary events of an experiment is one.