Visualization of Sample Space through Concepts of Functions and Relations

Sample Space: Sample Space is the set of all possible outcomes of an experiment. The set of Favorable cases is a subset of the Sample Space. While computing the probability we should visualize the sample space. For a single discrete random variable this sample space can be listed. A random variable is a function of this sample space. This is illustrated by the following example.

Example: Getting a face 6 in a roll of a die

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

Outcome: Getting a Six

Random variable X denotes getting a face 6 in a single roll of a die.

X = 0, 1

This is same as saying,  

X = not getting six, getting six

P(not getting six) = 5/6

P( getting six) = 1/6
The figure above shows the mapping from Sample Space to Probability Space