The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
Revision on Probability - grade C
1.
Chloe records the number of goals scored by her favourite football team in each of 40 matches.
Number of goals
Frequency
0
7
1
15
2
13
3
2
4
2
5
1
(a)
Chloe’s father watched one of these matches on TV.
What is the probability that the team scored at least one goal in that match?
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Answer .........................................................................
(2)
(b)
Calculate the mean number of goals scored per match.
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Answer .........................................................................
(3)
(Total 5 marks)
2.
In a sixth form college there are 1000 students.
2 of the students are girls.
5
The probability that a girl chosen at random studies mathematics is 1
10
The probability that a boy chosen at random studies mathematics is 1
6
The Robert Smyth School
1
The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
Calculate how many students in the college study mathematics.
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Answer ..................................................students
(Total 4 marks)
3.
Chandni wants to survey pupils in her school about their reading habits.
(a)
Write a question that would help Chandni to investigate how often pupils in her school
read for pleasure.
Include a response section.
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(2)
(b)
There are 1000 pupils in Chandni’s school.
Chandni samples 50 pupils at random and asks them to complete her survey.
She finds that 16 of the pupils in the sample read comics.
Estimate the number of pupils in the school who read comics.
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Answer ............................................................
(2)
(Total 4 marks)
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
4.
A bag contains 12 blue and 8 green counters.
More blue and green counters are added to the bag such that for every blue counter added, two
green counters are added.
1
The probability that a counter taken at random is blue is now
2
How many blue and green counters were added to the bag?
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Answer ................... blue ................. green
(Total 2 marks)
5.
The probabilities of whether a student, picked at random from a school, is vegetarian or not are
shown in this table.
Vegetarian
Non-vegetarian
(a)
Boys
Girls
0.08
0.4
0.2
0.32
What is the probability that a student chosen at random from the school is vegetarian?
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Answer ............................................
(1)
(b)
There are 320 girls in the school who are vegetarian.
How many students are there in the school altogether?
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Answer ................................ students
(2)
(Total 3 marks)
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
6.
Penny, Sam and Robert do this experiment on the same bag of 10 counters.
1. Take a counter from the bag at random.
2. Record its colour.
3. Put the counter back in the bag.
Repeat this trial a number of times.
Their results are shown in this table.
Colour of counter
Name of
pupil
Number
of trials
Black
White
Green
Penny
10
0
6
4
Sam
40
3
16
21
Robert
200
22
76
102
Estimate the number of each different coloured counter in the bag.
Clearly state the set of results that you use to make the estimate.
Give a reason for your choice.
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Set of results used .....................................................
Reason .................................................................................................................................
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Answer Black ......................., White ......................., Green ………………….
(Total 4 marks)
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
1.
(a)
15 + 13 + 2 + 2 + 1 or 40 – 7
=
(b)
M1
33
40
A1
(0 × 7) + 1 × 15 + 2 × 13 + 3 × 2 + 4 × 2 + 5 × 1
Or (0) + 15 + 26 + 6 + 8 + 5
Attempt at fx or total 58 to 63 or 67
0 × 7 need not be included
“60”  40
M1
M1 dep
= 1.5
A1
Ans only of 1.675
SC1
[5]
2.
2
× 1000 or 400 (girls)
5
or
M1
3
× 1000 or 600 (boys)
5
Alternative method
2 1
2

or
5 10
50
1 3
3
or
 or
6 5
30
1
× 400 or 40 girls
10
2
× 1000 or 40 girls
50
1
× 600 or 100 boys
6
3
× 1000 or 100 boys
30
140 students
M1
M1
A1
[4]
3.
(a)
(b)
Eg.
How often do you read for pleasure?
Time related and reading for a purpose
B1
Response section eg.
Daily (frequently)
Every 2 or 3 days (often)
Weekly (sometimes)
About once a month (rarely)
Never
Choice of time categories only
B1
16/50 × 1000
M1
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The Robert Smyth School
Mathematics Faculty
Topic 1
Probability
Innovation & excellence
320
A1
[4]
4.
4 blue and 8 green
M1,A1
M1 for attempt to find a solution (e.g. T&I)
A1 answer
[2]
5.
(a)
0.28
B1
Accept equivalent fractions or 28%
(b)
320  0.2
M1
M1 for equating 320 with 0.2
= 1600
A1
[3]
6.
Robert's results
B1
or all results
Largest number of trials
( 22
200
or 76
200
or 102
B1
200
) × 10
M1
or (25/250 or 98/250 or 127/250) × 10
allow rounded values
or black =1 or white = 4 or green = 5
or 1/10 and 4/10 and 5/10
black = 1, white = 4, green = 5
A1
[4]
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