statistics AND probability • chance
reasoning
8 In how many different ways can change be given for a 50 cent coin using only 20 cent, 10 cent
and 5 cent coins?
9 Sabita remembered that her mother’s car registration
plate had 2 letters followed by 3 digits. She recalled
that the let­ters were S and C and that the digits were 8,
3 and 7 but couldn’t remember the order. What
combination of letters and numbers could her mother’s
car registration plate have? Make a list of the
possibilities.
10C
reflection  
Are all elements in a sample
space equally likely to occur?
Simple probability
■■
■■
■■
An outcome is a particular result of an experiment.
A favourable outcome is one that we are looking for.
The theoretical probability of a particular result or event is defined as
P(event) =
number of favourable outcomes.
number of possible outcomes
Worked Example 5
State how many possible outcomes there are for each of the following experiments
and specify what they are:
a tossing a coin
b spinning a circular spinner with 9 equal sectors labelled from a to i as shown
at right
c drawing a picture card (jack, king, queen) from a standard pack of cards.
Think
a
b
c
1
Make a note of how many sides the coin has
and what each side represents.
2
Answer the question.
1
Make a note of how many sectors the
circular spinner has and what each one
represents.
2
Answer the question.
1
Make a note of how many picture cards
there are and what they are.
2
362
Answer the question.
Maths Quest 7 for the Australian Curriculum
Write
a The coin has 2 sides, a Head and a Tail.
When tossing a coin there are two possible
outcomes; they are Head or Tail.
b The circular spinner has 9 sectors labelled
a to i.
When spinning the circular spinner, there are
9 possible outcomes; they are a, b, c, d, e, f, g, h
or i.
c There are 3 picture cards in each of the four
suits.
When drawing a picture card there are
12 possible results; they are: the jack, king and
queen of clubs, the jack, king and queen of
diamonds, the jack, king and queen of hearts
and the jack, king and queen of spades.
statistics AND probability • chance
Worked Example 6
Christopher rolls a fair 6-sided die.
a What are all the possible results that could be obtained?
b What is the probability of obtaining:
i a 4?
ii a number greater than 2?
iii an odd number?
Think
Write
a Write all the possible outcomes and answer
a There are six possible outcomes; they are 1, 2,
3, 4, 5, 6.
the question.
b
i
ii
iii
1
Write the number of favourable
outcomes. A 4 occurs once. Write the
number of possible outcomes.
b
i Number of favourable outcomes = 1
Number of possible outcomes = 6
number of favourable outcomes
P(event) =
number of possible outcomes
2
Write the rule for probability.
3
Substitute the known values into
the rule and evaluate.
4
Answer the question.
The probability of obtaining a 4 is 16 .
1
Write the number of favourable
outcomes and the number of
possible outcomes.
Note: ‘Greater than 2’ implies 3,
4, 5, 6.
P(4) = 16
ii Number of favourable outcomes = 4
Number of possible outcomes = 6
2
Substitute the known values
into the rule for probability and
evaluate.
P(greater than 2) =
4
6
3
Simplify the fraction.
=
2
3
4
Answer the question.
The probability of obtaining a number
greater than two is 23 .
Repeat steps 1 to 4 of part b ii.
Note: ‘An odd number’ implies 1, 3, 5.
iii Number of favourable outcomes = 3
Number of possible outcomes = 6
P(an odd number) = 63
=1
2
The probability of obtaining an odd number
is 1 or 50%.
2
remember
The probability of a particular result or event is defined as the number of favourable
outcomes divided by the number of possible outcomes. This is written as:
number of favourable outcomes.
P(event) =
number of possible outcomes
Chapter 10 Probability
363
statistics aND Probability • ChanCe
exerCise
10c
individUal
paThWaYs
eBook plus
Activity 10-C-1
Pick that card A
doc-6534
Activity 10-C-2
Pick that card B
doc-6535
Activity 10-C-3
Pick that card C
doc-6536
simple probability
flUenCY
1 We5 State how many possible outcomes there are for each of the following experiments and
specify what they are.
Rolling a 12-sided die, numbered 1 to 12 inclusive
Spinning a spinner for a game that has 5 equal-sized sections, numbered 1 to 5 inclusive
Choosing a consonant from the word ‘cool’
Choosing a sock out of a drawer containing 3 different socks coloured red, blue and black
Picking a marble out of a bag containing 5 different marbles coloured black, blue, green,
red and yellow
f Rolling an even number on a fair 6-sided die
g Rolling an even number greater than 2 on a fair 6-sided die
h Choosing an odd number from the first 20 counting numbers
2 List all the possible results in the following experiments. Comment on whether all results in
each case are equally likely. Explain your answer.
a Rolling a fair 6-sided die
b Tossing a normal coin
c Spinning a spinner where half is white and half is black
d Spinning a spinner where half is white, a quarter is blue and a quarter is red
e Rolling a 6-sided die that has the numbers 1, 2, 3, 4, 5, 5 on it
1
1
1
f Shooting at a target where of the area is blue, green and red
3
3
3
g Choosing a vowel in the word ‘mathematics’
3 We6 Christina rolls a fair 10-sided die with faces numbered from 1 to 10.
a What are all the possible results that could be obtained?
b What is the probability of obtaining:
i a 9?
ii a number less than 7?
iii a prime number?
iv a number greater than 3?
v a multiple of 3?
vi a number greater than 10?
vii an even number greater than 4?
viii an odd number divisible by 3?
a
b
c
d
e
4 Leo has been given a bag of marbles to play with. Inside the bag there are 3 blue, 6 red, 4 green
and 7 black marbles.
a How many marbles are in the bag?
b If Leo takes out one marble from the bag what is the:
i P(getting a red marble)?
ii P(getting a green marble)?
iii P(getting a black marble)?
iv P(getting a blue marble)?
364
maths Quest 7 for the australian Curriculum