We want to describe the way we can test theoretical probability using sample data. To do so, let's consider an example of rolling a die.

Now, let's conduct an experiment to estimate the probability of rolling

6 .

We will use the above simulator and test different sample sizes. Here, the experimental probability will be the number of times

6

appears divided by the total number of rolls.

Number of Rolls	Number of Times $6$ Appears	Experimental Probability
$10$	$3$	$\frac{3}{1 0}$ or $30 %$
$20$	$2$	$\frac{2}{2 0}$ or $10 %$
$50$	$7$	$\frac{7}{5 0}$ or $14 %$
$100$	$16$	$\frac{1 5}{1 0 0}$ or $16 %$
$1000$	$163$	$\frac{1 6 3}{1 0 0 0}$ or $16.3 %$

The theoretical probability of rolling

6

on a die is

\frac{1}{6}

because we have

1

favorable outcome — the number

6

— and

6

possible outcomes.

Theoretical Probability = \frac{1}{6} \approx 16.7 %

According to the table, the greater the number of rolls is the closer the experimental probability gets to the theoretical probability. Therefore, by calculating an experimental probability using the sample data we can test if we evaluated a theoretical probability correctly. However, remember that we will obtain better results if we use larger samples.

Exercise