The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
Homework on Probability scale and listing outcomes
1.
The probabilities of the following events have been marked on the probability scale
below.
A: The next person to pass you will be less than 80 years old.
B: Tomorrow will be Sunday.
C: A fair three-sided spinner, coloured red, blue and green, will land on red.
0
1
Label each arrow with a letter to show which event it represents.
(2)
2.
A fair six-sided dice is thrown once.
The probabilities of the following events have been marked on the probability scale
below.
A:
An even number is thrown.
B:
A ‘7’ is thrown.
C:
A number less than 5 is thrown.
0
1
Label each arrow with the letter to show which event it represents.
(Total 3 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
3.
There are 10 beads in a bag. Three beads are green, three are red and four are
yellow. One bead is taken out of the bag at random.
The probabilities of three events have been marked on the probability scale below.
A: The bead is yellow.
B: The bead is white.
C: The bead is not red.
0
1
Label each arrow with the letter to show which event it represents.
(Total 3 marks)
A fair spinner has five sections.
Two sections are red, one is white, one is black and one is yellow.
k
ac
Bl
Red
Yello
w
Re
d
4.
White
The spinner is spun once.
(a)
Which colour is the spinner most likely to land on?
Answer ...........................................
(1)
(b)
The probabilities of three events have been marked on the probability scale
below.
A: The spinner lands on red.
B: The spinner lands on white.
C: The spinner does not land on yellow.
0
1
Label each arrow with a letter to show which event it represents.
(3)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
5.
Danny has two fair spinners.
Spinner A has four equal sections, two are red, one is yellow and one is green.
Spinner B has six equal sections, three are red, one is yellow and two are green.
red
yellow
red
green
red
green
yellow
red
red green
Spinner A
Spinner B
Danny spins each spinner once.
(a)
Which colour is Spinner A most likely to land on?
Answer ................................................
(1)
(b)
Which spinner is more likely to land on yellow, Spinner A or Spinner B?
Give a reason for your answer.
.....................…………………………………………………………………………
.....................…………………………………………………………………………
(1)
(c)
What is the probability that Spinner A lands on green?
Answer ................................................
(1)
(d)
The probabilities of three events have been marked on the probability scale
below.
R:
Y:
G:
Spinner B lands on red
Spinner B lands on yellow
Spinner B lands on green
0
1
Label each arrow with a letter to show which event it represents.
(2)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
6.
A game involves choosing tiles from a bag.
There are six tiles in the bag, as shown.
A X T E X
Chris chooses two tiles at random from the bag.
(a) List all the possible outcomes of choosing two tiles.
................................…………………………………………………………………………
................................…………………………………………………………………………
(3)
(b) What is the probability that they have different letters?
................................…………………………………………………………………………
Answer ................................................
(2)
7.
(a)
There are four socks in a drawer.
A
(i)
B
C
D
Two socks are chosen at random.
One possible choice is A and B.
Write down the other five possible choices.
...........................................................................................
...........................................................................................
(ii)
Two of the socks in the drawer are white and two are black.
If two of these four socks are chosen at random, what is the probability
that a black pair will be chosen?
...........................................................................................
...........................................................................................
(3)
(b)
Another drawer contains red socks and green socks.
The probability of choosing a red pair is 0.33.
What is the probability that a red pair will not be chosen?
..................................................................................................
..................................................................................................
(1)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
Answers - Topic 1 – Homework on Probability scale
and listing outcomes
1.
B, C, A
B2
Any 1 correct
B1
[2]
2.
Note: Probability - Accept fraction, decimal or percentage. Do not accept ratio.
eg 1 out of 3 or 1 in 3 penalise once on whole paper.
BAC
B3
B1 for each correct label
[3]
3.
BAC
B3
B1 for each correct label
[3]
4.
(a)
Red
(b)
B, A, C
B1
B3
Fully correct. B1 each correct
Allow W R N or W R Y
[4]
5.
(a)
Red
B1
(b)
A: ‘1 out of 4’ is more than ‘1 out of 6’
(Need not use probabilities).
‘A’ with valid reason
Accept: It has less colours
Identifying 4 sections for A and 6 for B
Comparing sizes of angles.
B1
(c)
1
or 0.25 or 25%
4
B1
(d)
YGR
B2
1 (or 2) correct
B1
[5]
6.
(a)
(b)
AX
XA
TA
EA
XA
AT
XT
TX
EX
XX
AE
XE
TE
ET
XT
(AX)
XX
(TX)
(EX)
XE
9
10
B3 -1ee
numeratorA1ft
denominator A1ft
[5]
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
7.
(a)
(b)
(i)
AC
AD
BC
CD
BD
Ignore any repeats or permutations
(ii)
Use of 6 as a denominator
answer: 1/6 or 0.16, 0.17
M1 only: 1:6:1 in 6, 16%, 17%
No follow through for M or A
B1
M1
A1
2/4 × 1/3 M1
= 2/12
A1
0.67
B1
0.66 scores B0
2
/3 scores B0 67% B0
[4]
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