## DEMONSTRATION OF THE RELATIVE FREQUENCY NOTION OF PROBABILITY

Suppose I toss two fair dice and I'm interested in the probability that the sum of the two faces is equal to 6. I can use the computer to simulate this experiment a large number of times. As I simulate dice rolls, I keep track of the number of "sums of 6" I observe and the relative frequency

```                   number of sixes
---------------  .
number of tosses
```
On the computer I toss two dice 1000 times. On the graph below, I plot the relative frequency of "sum of 6" against the number of experiments.

Note that there is a lot of variation in the relative frequencies for a few experiments. As I toss the dice more times, the relative frequencies appear to settle down. I would guess from the graph that the true probability that I get a sum equal to 6 is just under .15. In fact, the actual probability is equal to .139.

Page Author: Jim Albert (© 1996)
albert@bayes.bgsu.edu
Document: http://www-math.bgsu.edu/~albert/m115/probability/dice.html
Last modified: November 24, 1996