5.5 Estimating probability

When you don’t know enough about a population to calculate the theoretical probability, you can estimate the probability using the relative frequency from a sample of the population.

For example:a bag contains some red and some blue sweets. There are 7 red sweets and 3 blue sweets.

Amrit does not know how many sweets of each colour are in the bag.

She took out one sweet from the bag, recorded its colour and replaced it.

Amrit did this 10 times and found that she picked a red sweet 5 times. This gave the relative frequency .

At this point Amrit predicted that the probability of picking a red sweet was , or ½. Therefore, if there were 10 sweets in the bag in total, she thought there were probably 5 red sweets.

In order to get a more accurate estimate of the probability, Amrit should repeat the experiment many more times.

As we discussed earlier, the more times an experiment is carried out, the closer the relative frequency will be to the theoretical probability.