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# What is a sample space?

Module by: Christopher Chikalimba-Gama. E-mail the author

Summary: This module defines what a sample space is and its examples.

A sample space is a set or collection of outcome of a particular random experiment.

For example, imagine a dart board. You are trying to find the probability of getting a bullseye. The dart board is the sample space. The probability of a dart hitting the dart board is 1.0. For another example, imagine rolling a six sided die. The sample space is {1, 2, 3, 4, 5, 6}.

The following list consists of sample spaces of examples of random experiments and their respective outcomes.

• The tossing of a coin, sample space is {Heads, Tails}
• The roll of a die, sample space is {1, 2, 3, 4, 5, 6}
• The selection of a numbered ball (1-50) in an urn, sample space is {1, 2, 3, 4, 5, ...., 50}
• Percentage of calls dropped due to errors over a particular time period, sample space is {2%, 14%, 23%, ......}
• The time difference between two messages arriving at a message centre, sample space is {0, ...., infinity}
• The time difference between two different voice calls over a particular network, sample space is {0, ...., infinity}

## Exercise 1

What is the sample space of the buttered toast random experiment?

### Solution

The sample space of the buttered toast example will be:

{Buttered side up, Buttered side down}

## Reference

1. Ali M. Probalistic system analyses: Part I. University of the witwatersrand, 2000.
2. http://www.atsweb.neu.edu/chance/book/basic_definitions.html

Co-Author: Brandon Hodgson

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