15 Relative Frequency And Probability Examples And Worksheets - Maths Quest General Maths Preliminary Course Page 3
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30Relative frequency
15a
You are planning to go skiing on the fi rst weekend in July. The trip is costing you a lot of money
and you don’t want your money wasted on a weekend without snow. So what is the chance of it
snowing on that weekend? We can use past records to estimate that chance.
If we know that it has snowed on the fi rst weekend of July for 54 of the last 60 years, we
could say that the chance of snow this year is very high. To measure that chance, we calculate
the relative frequency of snow on that weekend. We do this by dividing the number of times
it has snowed by the number of years we have examined. In this case, we can say the relative
frequency of snow on the fi rst weekend in July is 54 ÷ 60 = 0.9.
The relative frequency is usually expressed as a decimal and is calculated using the formula:
number of times an event has occured
Relative frequency =
number of trials
In this formula, a trial is the number of times the probability experiment has been conducted.
WORKED EXaMPLE 1
The weather has been fi ne on Christmas Day in Sydney for 32 of the past 40 years. Calculate the
relative frequency of fi ne weather on Christmas Day.
THINK
WRITE
number of times an event has occured
Relative frequency =
1
Write the formula.
number of trials
32
Relative frequency =
2
Substitute the number of fi ne
40
Christmas Days (32) and the number
of trials (40).
= 0.8
3
Calculate the relative frequency as a
decimal.
The relative frequency is used to assess the quality of products. This is done by fi nding the
relative frequency of defective products.
WORKED EXaMPLE 2
A tyre company tests its tyres and fi nds that 144 out of a batch of 150 tyres will withstand 20 000 km
of normal wear. Find the relative frequency of tyres that will last 20 000 km. Give the answer as a
percentage.
THINK
WRITE
number of times an event has occured
Relative frequency =
1
Write the formula.
number of trials
144
Relative frequency =
2
Substitute 144 (the number of times
150
the event occurred) and 150 (number
of trials).
= 0.96
3
Calculate the relative frequency.
= 96%
4
Convert the relative frequency to a
percentage.
481
Chapter 15
Relative frequency and probability
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