Estimating probability

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In an experiment or survey, relative frequency of an event is the number of times the event occurs divided by the total number of trials.

For example, if you observed \(100\) passing cars and found that \(23\) of them were red, the relative frequency would be \(\frac{23}{100}\).

Accuracy

The Probability learner guide describes how you can get a more accurate result in surveys of events if you carry out a large number of trials or survey a large number of people.

Example

Bag containing 3 red sweets and 7 blue sweets

This bag contains \({3}\) red sweets and \({7}\) blue sweets.

Tom took a sweet from the bag, noted its colour and then replaced it.

He did this \(10\) times and found that he obtained a red sweet on \(4\) occasions, so the relative frequency of the event that a red sweet was chosen is \(\frac{4}{10}\).

He then carried out the experiment another \({10}\) times and combined his results with the first trial. He found that he had obtained a red sweet on \(5\) out of \(20\) occasions, so the relative frequency of the event that a red sweet was chosen was \(\frac{5}{20}\).

Tom continued in this way, recording his combined results after every \({10}\) trials and plotting them on the graph below:

Relative frequency graph

We can see from the graph that relative frequency gets better (ie closer to the true probability) as the number of trials increases.