A more accurate estimate of probability
In order to get a more accurate estimate of the probability, we would need to look at a greater number of trials.
Example
Let’s imagine we have a bag containing two different types of sweet but we do not know how many of each sweet there is.
If we took a sweet from the bag 10 times – putting the sweet back after each look – and we found that we obtained a red sweet 4 times out of 10, then the relative frequency would be \(\frac{4}{10}\). We would estimate that the probability of getting a red sweet was \(\frac{4}{10}\) or 0.4.
If we then repeated this another 10 times, and only got one red sweet, we could combine our results to get a new relative frequency of \(\frac{5}{20}\) and therefore a new estimate of the probability of getting a red sweet as \(\frac{5}{20}\) or 0.25.
If we looked inside the bag, we could see that the true probability is \(\frac{3}{10}\) or 0.3 as there are 3 red sweets out of a total of 10 sweets, so our estimate was not far off.
When using relative frequency to estimate probability, it is important to note that the larger the number of trials, the more accurate the estimate is likely to be.
If we continued taking sweets from the bag in lots of 10 and plotted a graph of our results, we may expect to see something that looks like this:
This is how we represent relative frequency against the number of trials graphically. As the number of trials increases so too should the stability of the graph.
