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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.

Return to AN INTRODUCTION TO PROBABILITY

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