Statistics - Probability


Probability implies 'likelihood' or 'chance'. When an event is certain to happen then the probability of occurrence of that event is 1 and when it is certain that the event cannot happen then the probability of that event is 0.

Hence the value of probability ranges from 0 to 1. Probability has been defined in a varied manner by various schools of thought. Some of which are discussed below.

Classical Definition of Probability

As the name suggests the classical approach to defining probability is the oldest approach. It states that if there are n exhaustive, mutually exclusive andequally likely cases out of which m cases are favourable to the happening ofevent A,

Then the probabilities of event A is defined as given by the following probability function:


${P(A) = \frac{Number\ of\ favourable\ cases}{Total\ number\ of\ equally\ likely\ cases} = \frac{m}{n}}$

Thus to calculate the probability we need information on number of favorable cases and total number of equally likely cases. This can he explained using following example.


Problem Statement:

A coin is tossed. What is the probability of getting a head?


Total number of equally likely outcomes (n) = 2 (i.e. head or tail)

Number of outcomes favorable to head (m) = 1

${P(head) = \frac{1}{2}}$