St Patrick’s College, Shorncliffe
Mathematical Methods
Name
Teacher
Date: Term 3, Week 8
Instrument
Technique
Examination (formative)
Unit
Prep Unit B
Topics
Probability
Instrument
no.
n/a
Conditions
Time
45 minutes
Permitted
equipment
 Year 10 Formula sheet may be used
 Black or blue pens, ruler, eraser (no pencils)
 Calculators are permitted
Perusal
5 minutes
Instructions
 Show all working in the spaces provided.
 Write responses using black or blue pen only. (No pencils)
 Unless otherwise instructed, all numerical answers should be given in simplest form.
Criterion
Foundational knowledge and problem solving
Assessment objectives 1, 2, 3, 4, 5, 6
Result
Stanine
/35
Reflection
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Instrument-specific marking guide
Criterion: Foundational knowledge and problem-solving
Assessment objectives
1.
select, recall and use facts, rules, definitions and procedures drawn from all topics
2.
comprehend mathematical concepts and techniques drawn from all topics
3.
communicate using mathematical, statistical and everyday language and conventions
4.
evaluate the reasonableness of solutions
5.
justify procedures and decisions by explaining mathematical reasoning
6.
solve problems by applying mathematical concepts and techniques drawn from all topics
Examination marks summary
Paper 1
Q1
Q2
Q3
Q4
Q5
Item type
MC
SR
SR
SR
SR
Marks (SF)
Marks (CF)
Marks (CU)
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/8
/6
/7
/7
/7
Paper 1
Question 1a (SF)
(1 mark)
Consider a set of cards numbered 1 to 10. If one card is chosen, what is the probability it will
be an even number?
1
A 5
2
B 5
1
C 2
3
D 10
Question 1b
(1 mark)
A coin is flipped three times. How many different outcomes are there?
A 2
B 4
C 6
D 8
Question 1c
(1 mark)
One card is drawn from a deck of cards and its suit is noted. It is replaced, then a second card
is drawn. What is the probability two diamonds are drawn?
1
A 13
1
B 16
1
C 17
3
D 52
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Question 1d
(1 mark)
The Venn diagram below shows the number of students that study French and Spanish at a
school.
If a student is picked at random, what is the probability that they study Spanish?
A
11
34
19
B 34
11
C 40
19
D 40
Question 1e
(1 mark)
If a student is picked at random, what is the probability that they study French but not
Spanish?
A
B
C
D
15
34
23
34
15
40
23
40
Question 1f
Which area of the following Venn diagram is
highlighted?
A 𝐴 ∩ 𝐵′
B 𝐴′ ∩ 𝐵
C 𝐴 ∪ 𝐵′
D 𝐴′ ∪ 𝐵
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(1 mark)
Question 1g
(1 mark)
If the probability that it will rain tomorrow is 60%, what’s the probability that it won’t rain?
A 0
B 0.4
C 0.6
D 1
Question 1h
(1 mark)
The condition for two events to be independent is:
A 𝑃(𝐴) + 𝑃(𝐵) = 1
B 𝑃(𝐴|𝐵) = 𝑃(𝐴)
C 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) × 𝑃(𝐵)
D 𝑃(𝐴) = 𝑃(𝐵)
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Formative exam (technology-act)
Question 2 (SF)
(6 marks)
The table below shows subjects studied by 150 students at a school.
A student from the school is selected at random. Let � be the event the student studies French. Let �
be the event the student is in Year 11.
a) Determine 𝑃(French Student).
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a) Determine the probability that the student is in Year 11, given that they study French.
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b) Are the events 𝐹 and 𝑌 independent? Justify your decision.
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Formative exam (technology-active)
Question 3 (SF)
(7 marks)
An urn contains 10 balls: two green, three red and five blue. Two balls are drawn at random, without
replacement, one after another from the urn.
a) Draw a probability Tree for this experiment.
b) Find the probability (to two decimal places) that exactly one of the balls is green
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c) Find the probability (to two decimal places) that both balls have the same colour
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Formative exam (technology-active)
Question 4 (CF)
(7 Marks)
The Australian Cancer Council conducted a survey to investigate the amounts of cancer around the
whole nation, and which figure out which state has the greater risk.
Data was collected on 11,985 skin clinic patients in Queensland and Victoria.
The study found that 10,393 people reported they had skin cancer, the highest amount being 6,341
in Victoria. Of the 4,385 Queenslanders surveyed, 333 reported no skin cancer.
Use the given data to determine whether an association exists between a person’s state of residence
and skin cancer. By identifying one potential source of bias, evaluate the limitations of any conclusions
drawn.
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Formative Quiz (technology-active)
Question 5 (CU)
(7 marks)
Lucas uses only two modes of transport to travel between his home and his school: his bicycle
or the bus. If the weather is nice, Lucas uses his bicycle 9 times out of 10. If the weather is
poor, he only uses his bicycle 4 times out of 10.
Let p be the probability that the weather is nice, on a given day, where Lucas lives.
Given that the probability that Lucas does not use his bicycle to go to school is 0.33,
calculate the probability that the weather is nice (p).
Justify your answer using a diagram.
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