Probability Example

Graph of approximations to the probability of getting 1 on a toss of a fair die

This graph illustrates the empirical definition of probability. The horizontal axis shows the number of tosses of a fair die. The vertical axis shows the proportion of those tosses which came up 1.  (These are also shown in the table below.) The trend of the graph is that as the number of tosses increases, the proportion of ones approaches the true probability of 1/6 = 0.16666... . Notice that the zeroing in on the true value is not steady -- in this particular simulation, there is some moving upward from 800 to 1000. However, if we increased the number of tosses to 2000, 3000, etc., we would expect the calculated proportions to  vary less and less from the true value.

Number of Tosses Proportion of Ones
100 0.19
200 0.19
300 0.18333...
400 0.1825
500 0.182
600 0.18
700 0.177142857
800 0.17125
900 0.1744...
1000 0.175