In this section we compare *theoretical* and *experimental* probabilities.

The term 'theoretical probabilities' describes those which have been calculated, for example by the methods described in sections 6.2. and 6.3.

'Experimental probabilities' are estimates for probabilities that cannot be determined logically. They can be derived from the results of experiments, but often they are obtained from the analysis of statistical data or historical records.

Here we obtain experimental probabilities from simple experiments and compare them with the theoretical probabilities.

An unbiased dice is to be rolled 240 times.

(a)

Calculate the number of times you would expect to obtain each of the possible scores.

p(6) = |

Expected number of 6s = | × 240 = 40 |

(b)

Now roll the dice 240 times and collect some experimental results, presenting them in a bar chart.

The results of the experiment are recorded in the following table:
These results are illustrated in the following bar chart. A horizontal line has been drawn to show the expected frequencies for the scores.

Note that none of the bars is of the expected height; some are above and some are below. However, all the bars are *close* to the predicted number.

We would not expect to obtain *exactly* the predicted number. The more times the experiment is carried out, the closer the experimental results will
be to the theoretical predictions.