Unit 21 Section 3 : Relative Frequency

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:

We can estimate the probability of a particular outcome by calculating the relative frequency.
The estimate of probability becomes more accurate if more trials are carried out.

Example 2
Matthew decides to try to estimate the probability that toast lands butter-side-down when dropped.
He drops a piece of buttered toast 50 times and observes that it lands butter-side-down 30 times.

He wants to estimate the probability that the toast lands butter-side-down.
The relative frequency of the toast landing butter side down is .
He would therefore estimate that the probability of the toast landing butter-side-down 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

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

 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:

In this exercise, you must also simplify the fractions in your answers.
Question 1
A drawing pin can land 'point up' or 'point down' when dropped.
Jim drops a drawing pin 100 times and it lands "point up" 35 times.

Estimate the probability of the drawing-pin landing "point up"

Question 2
A six-sided dice was rolled 120 times.
The "1" occurred 24 times.

Estimate the probability of getting "1" on this dice.

Question 3
Jane asked 30 people whether they were left-handed or right-handed.
4 people said they were left-handed.

Estimate the probability of any person chosen at random being left-handed.

Question 4
Sheila flipped a biased coin 150 times.
The coin landed on "heads" 121 times.

Estimate the probability of the coin landing on "tails".

Question 5
It rained on 12 days in November last year.

Estimate the probability that it will rain on 20 November next year.

Question 6
A calculator can be used to generate random digits. Halim generates 100 random digits with his calculator.
He lists the results in the table below.
Based on Halim's results, estimate the probability that the calculator produces:
 (a) a "9" (b) a "2" (c) an odd number (d) a number less than 3

Question 7
Tony estimates that the probability that there will be an empty space in the car park when he arrives at work is .
His estimate is based on 50 observations.

On how many of these 50 days was he unable to find an empty space in the car park?
days

Question 8
Paul draws the bar chart on the right to show the
results for his football team so far this season.

Estimate the probability that his team will win their next match.

You have now completed Unit 21 Section 3
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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