# Probability Model

## Definition of Probability Model

A probability model is any mathematical representation of a random phenomenon. It comprises of a sample space, events and the probabilities of the each event.

## Sample Space

A sample space is the set of all possible outcomes. For instances if we are to roll a dice ,there are a total of 6 sides namely 1,2,3,4,5 and 6. Therefore, the sample space for a dice would be S={1,2,3,4,5,6}. Additionally, if we have 5 T-shirts with different colors in a basket one yellow, one red, one green, one blue and one violet.. The sample space S= {yellow, red, green, blue, violet}.

## Events

An event in probability and statistics is a subset of a given sample size. For instance, if there are 5 marbles in a box; 3 yellow and 2 green. If one is to pick 3 balls randomly, the event that they will pick 2 yellow ones can be expressed in 3 sets of comes

A= {(yellow, yellow, green), (yellow, green, yellow), (green, yellow, yellow)}.

The sample space (all possible outcomes) on the other hand will be

S={(yellow, yellow, green), (yellow, green, yellow), (green, yellow, yellow),(yellow,yellow,yellow),(green,green,yellow),(green,yellow,green),(yellow,green,green)}

## What is Probability in a probability Model?

It is a numeric value which quantifies the likelihood that a given event will occur. The probability of any event, say A, is written as P (A).

The probability of any event is usually calculated as shown below

## Basic Rules of Probability

1. The probability of any event is between 0 and 1 such that 0 ≤ P (A) ≥ 1.
2. The probability of any sample space is 1, i.e. P(S) = 1.For instance in the case of a dice, there are 6 sides hence the sample space will be S= {1, 2, 3, 4, 5, 6}.each with a probability of  1/6 hence the total probability will be (1/6)*6=1
3. If two events, say A and B are disjoint, then the probability of the two events will be calculated P (A or B) = P (A) +P (B).Disjoint events are events which do not have common items.
4. The probability that any event will not occur is P (Ac) = 1-P (A).