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.