Describing categorical and discrete populations
Categorical and discrete samples can be described graphically with bar charts of the proportions for the distinct values. Since probabilities are defined to be population proportions, the underlying population can also be described by a bar chart.
Bar charts and the law of large numbers
The law of large numbers states that sample proportions approach the underlying probabilities as the sample size increases. This means that a sample bar chart will be close in shape to the unknown population bar chart if the sample size is big enough.