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Relative frequency

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# Estimating probability

For an experiment or survey:

Relative frequency = number of times the event happens ÷ total number of trials

For example, if you observed 100 passing cars and found that 23 of them were red, the relative frequency is 23/100.

## Accuracy

In the Probability Revision Bite, you learnt that you 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

A 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 (ie the relative frequency was 4/10).

He then carried out the experiment another 10 times, combined his results with the first trial and saw that - in total - he had obtained a red sweet on 5 out of 20 occasions (ie the relative frequency was 5/20 ).

Tom continued in this way, recording his combined results after every 10 trials and showing them on the graph below:

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

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