# Finite Probability

Finite Probability is a very important concept in discrete mathematics. Before we begin let’s understand some basic terminology, that is important in understanding probability theory.

### Basic Terminologies

#### Experiment

An experiment is some task you do and get an outcome, possibly from a set of different outcomes. Example, throwing a dice would result in a number between one to six.

 THROW A DICE AND YOU GET A NUMBER

#### Sample Space

Sample space is all possible outcome an experiment. For example, throw a dice and you get the following outcomes.

Sample Space = { 1, 2, 3, 4, 5, 6 }

You cannot get more than the value of sample space.

#### Event

An event is a subset of sample space. It means desired outcomes from a set of sample space.
It is denoted in set notations as E ⊆ S. For example if you throw a dice, and a six to appear then it’s an event.
Probability is associated with the event and probability of an event is between 0 and 1. If a probability of an event is 1, then it is a certain event.

Probability of an event is denoted as P(E) and 0 < = P(E) <= 1.

#### Favorable Outcome

When an event occur then it is a favorable outcome when it happens.

#### Unfavorable Outcome

When the event does not happen then it is an unfavorable outcome as it did not happen. Sometimes, we also need to find unfavorable outcomes of an event.

#### Equally likely

An event is equally likely if the probability of each outcome in sample space is equally likely.

For example, when we toss a coin we get either Head or Tail out of two outcomes of the sample space. So there is a 50-50 chance of getting a Head or Tail and both are equally likely events.

 HEAD OR TAIL ARE EQUALLY LIKELY EVENTS

### Formal Definition of Probability

If S is a finite non-empty sample space of equally likely outcomes and E is an event, that is, a subset of S, then the probability of E is

P(E) = |E| / |S|

### Example Problem

Question :

A box contains 3 Red balls and 5 Green balls. What is the probability that a ball picked randomly from the box is Red?

Solution :

Total Number of Balls in Box =  3 + 5 = 8

Sample Space = 8

There are 3 ways to pick Red balls, Therefore, Event E = 3

P(E) = 3/8

The probability of picking a Red ball from the box is 3/8.