15 Relative Frequency And Probability Examples And Worksheets - Maths Quest General Maths Preliminary Course Page 8
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30INVESTIGaTE: Researching relative frequencies
Choose one of the topics below (or another of your choice)
and calculate the relative frequency of the event. Most of
the information needed can be found from books or the
Internet.
1
Examine weather records and find out the relative
frequency of rain on New Year’s Eve in Sydney.
2
Choose your favourite sporting team. Find the relative
frequency of them winning over the past three seasons.
3
Find the relative frequency of the stock market rising for
three consecutive days.
4
Check the NRL or AFL competitions and find the relative
frequencies of win, loss and draw for each team.
Single event probability
15B
In chapter 14 we discussed the chances of certain events occurring. In doing so, we used
informal terms such as probable and unlikely. While these terms give us an idea of whether
something is likely to occur or not, they do not tell us how likely they are. To do this, we need
an accurate way of stating the probability.
We stated earlier that the chance of any event occurring was somewhere between impossible
and certain. We also said that:
•
if an event is impossible the probability was 0
•
if an event is certain the probability was 1.
It therefore follows that the probability of any event must lie between 0 and 1 inclusive.
A probability is a number that describes the chance of an event occurring. All prob abilities
are calculated as fractions but can also be written as decimals or percentages. Probability is
calculated using the formula:
number of favourable outcomes
P(event) =
total number of outcomes
The total number of favourable outcomes is the number of different ways the event can occur,
while the total number of outcomes is the number of elements in the sample space.
WORKED EXaMPLE 4
Zoran is rolling a die. To win a game, he must roll a number greater than 2. List the sample space
and state the number of favourable outcomes.
THINK
WRITE
S = {1, 2, 3, 4, 5, 6}
1
There are 6 possible outcomes.
There are 4 favourable outcomes.
2
The favourable outcomes are to roll a 3,
4, 5 or 6.
Consider the case of tossing a coin. If we are calculating the probability that it will land Heads,
there is 1 favourable outcome out of a total of 2 possible outcomes. Hence we can then write
1
P(Heads) =
. This method is used to calculate the probability of any single event.
2
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