Some probabilities cannot be calculated by just looking at the situation.
For example, you cannot work out the probability of winning a football match by assuming that win, lose and draw are equally likely, but we can look at previous results in similar matches and use these results to estimate the probability of winning.
Example 1
The Bumbleton and Stickton village football teams have played each other 50 times.
Bumbleton have won 10 times, Stickton have won 35 times, and the teams have drawn 5 times.
We want to estimate the probability that Stickton will win the next match.
So far, Stickton have won 35 out of the 50 matches. We can write this as a fraction, which is
.
This fraction isn't the probability of Stickton winning, but it is an estimate of that probability.
We say that the relative frequency of Stickton winning is .
Relative frequency
We calculate the relative frequency of an outcome using this formula:
Example 2
Matthew decides to try to estimate the probability that toast lands buttersidedown when dropped.
He drops a piece of buttered toast 50 times and observes that it lands buttersidedown 30 times.
He wants to estimate the probability that the toast lands buttersidedown.
The relative frequency of the toast landing butter side down is .
He would therefore estimate that the probability of the toast landing buttersidedown is .
Practice Question
Work out the answers to the question below then click
to see whether you are correct.
Sarah tosses a coin 200 times. She gets 108 heads and 92 tails.
Using her results, estimate the probability of obtaining:
(a) a head when the coin is tossed
(b) a tail when the coin is tossed
Most of the answers in this section are fractions. Each fraction has two input boxes. Put the numerator in the top box and the denominator in the bottom box, like this: 
