Introduction: The basic to the study of probability is the idea of a Physical experiment. A single performance of the experiment is called a trial for which there is an outcome. Probability can be defined in three ways. The First one is Classical Definition. Second one is Definition from the knowledge of Sets Theory and Axioms. And the last one is from the concept of relative frequency.
Experiment:
Any physical action can be considered as an experiment. Tossing a coin, Throwing or rolling a die or dice and drawing a card from a deck of 52 cards are Examples for the Experiments.
Sample Space: The set of all possible outcomes in any Experiment is called the sample space. And it is represented by the letter s. The sample space is a universal set for the experiment. The sample space can be of 4 types.
They are: 1. Discrete and finite sample space.
2. Discrete and infinite sample space.
3. Continuous and finite sample space.
4. Continuous and infinite sample space.
Tossing
a coin, throwing a dice are the examples of discrete finite sample space. Choosing randomly a positive integer is an example of discrete infinite sample space. Obtaining a number on a spinning pointer is an example for continuous finite sample space. Prediction or analysis of a random signal is an example for continuous infinite sample space.
Event:
An event is defined as a subset of the sample space. The events can be represented with capital letters
like A, B, C etc… All the definitions and operations applicable to sets will apply to events also. As with sample space events may be of either discrete or continuous. Again the in discrete and continuous they may be either finite or infinite. If there are N numbers of elements in the sample space of an experiment then there exists 2N number of events.
The event will give the specific characteristic of the experiment whereas the sample space gives all the characteristics of the experiment.
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