Probabilities can be estimated from the results of an experiment.

We calculate the **relative frequency** of an event happening by working out the number of times it happened in relation to the total number of trials.

On the top (numerator) of the fraction, we place the number of times an option we are looking for has happened.

On the bottom (denominator) of the fraction, we place the total number of times we have carried out the experiment.

**Example**

A ball was drawn out of a bag and it's colour was noted down before it was replaced. This experiment was repeated many times.

The results were as follows.

Red 58

Blue 32

Green 10

Calculate the relative frequency that a blue ball was drawn out?

Estimate the probability of a green ball being drawn out in future.

**Answer**

The experiment was carried out 58 + 32 + 10 = 100 times.

32 out of 100 blue balls were drawn out.

This is a relative frequency of 32/100 = **8/25**

10 out of 100 green balls were drawn out.

This is a relative frequency of 10/100 = 1/10

Experimental probability of drawing out a green ball = **1/10**