# Statistics - Probability

## 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:

## Formula

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

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.

### Example

Problem Statement:

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

Solution:

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

Number of outcomes favorable to head (m) = 1

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