Probability Rules

A probability is a number assigned to the occurrence of an event in a sample space. Probability measures must satisfy three rules. If A is an event with probability denoted by P(A), then the following rules hold:

Rule 1

The probability of the entire sample space S is 1, i.e. P(S) = 1.

Area of sample space rectangle = 1. An event A is represented within the rectangle. Minimum possible area of A is 0 and maximum possible area is 1.

Rule 2

The probability of the event A must be greater than or equal to 0 and less than or equal to 1 or 100%, i.e. 0 < P(A) < 1. This rule says that probabilities cannot be negative and as the probability of the sample space is 1, the probability of an event contained in the sample space should be less than or equal to 1.

Rule 3

If A and B are mutually exclusive events, then the probability of (A or B) is equal to the sum of the probabilities of A and B.

P(A or B) =  P (A) + P (B) because P (A and B) = 0 as A and B are mutually exclusive.

Mutually exclusive events are those which do not overlap when represented in Venn diagrams.

Two events A and B are mutually exclusive if the occurrence of one implies the non-occurrence of the other. Hence obtaining a head on tossing a coin and obtaining a tail are mutually exclusive events.