Paper 3 June 2023, Question 11 1 mark
A and B are mutually exclusive events.
Which one of the following statements must be correct?
Tick (
) one box.
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AQA A Level Maths
Topic questions Statistics Mutually exclusive & independent events
Mutually exclusive & independent events
6 questions · 37 marks · about 45 minutes
Mutually exclusive and independent events questions
TopicMutually exclusive & independent events▾
AQA 7357 Mutually exclusive and independent events 6 questions
Paper 3 June 2022, Question 16 10 marks
Also involves Sets and Venn diagrams
A sample of 240 households were asked which, if any, of the following animals they own as pets:
The results are shown in the table below.
| Types of pet | C | D | T | C and D | C and T | D and T | C, D and T |
| Number of households | 153 | 70 | 45 | 48 | 21 | 32 | 17 |
(a)
[3]
Represent this information by fully completing the Venn diagram below.
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(b)
A household is chosen at random from the sample.
(b)(i)
[1]
Find the probability that the household owns a cat only.
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(b)(ii)
[2]
Find the probability that the household owns at least two of the three types of pet.
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(b)(iii)
[2]
Find the probability that the household owns a cat or a dog or both, given that the household does not own a tortoise.
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(c)
[2]
Determine whether a household owning a cat and a household owning a tortoise are independent of each other.
Fully justify your answer.
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Paper 3 November 2021, Question 14 7 marks
Also involves Sets and Venn diagrams
A and B are two events such that
(a)
[4]
Find P(A)
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(b)
[2]
Find P(B
A)
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(c)
[1]
Determine if A and B are independent events.
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Paper 3 November 2020, Question 13 6 marks
Diedre is a head teacher in a school which provides primary, secondary and sixth-form education.
There are 200 teachers in her school.
The number of teachers in each level of education along with their gender is shown in the table below.
| Primary | Secondary | Sixth-form | |
| Male | 9 | 24 | 23 |
| Female | 35 | 85 | 24 |
(a)
A teacher is selected at random. Find the probability that:
(a)(i)
[1]
the teacher is female
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(a)(ii)
[1]
the teacher is not a sixth-form teacher.
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(b)
[2]
Given that a randomly chosen teacher is male, find the probability that this teacher is not a primary teacher.
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(c)
[2]
Diedre wants to select three different teachers at random to be part of a school project.
Calculate the probability that all three chosen are secondary teachers.
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Paper 3 June 2019, Question 14 7 marks
A survey was conducted into the health of 120 teachers.
The survey recorded whether or not they had suffered from a range of four health issues in the past year.
In addition, their physical exercise level was categorised as low, medium or high.
50 teachers had a low exercise level, 40 teachers had a medium exercise level and 30 teachers had a high exercise level.
The results of the survey are shown in the table below.
| Low exercise | Medium exercise | High exercise | |
| Back trouble | 14 | 7 | 10 |
| Stress | 38 | 14 | 5 |
| Depression | 9 | 2 | 1 |
| Headache/Migraine | 4 | 5 | 5 |
(a)
Find the probability that a randomly selected teacher:
(a)(i)
[1]
suffers from back trouble and has a high exercise level;
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(a)(ii)
[2]
suffers from depression.
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(a)(iii)
[2]
suffers from stress, given that they have a low exercise level.
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(b)
[2]
For teachers in the survey with a low exercise level, explain why the events ‘suffers from back trouble’ and ‘suffers from stress’ are not mutually exclusive.
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Paper 3 June 2018, Question 14 6 marks
A teacher in a college asks her mathematics students what other subjects they are studying.
She finds that, of her 24 students:
12 study physics 8 study geography 4 study geography and physics
(a)
[2]
A student is chosen at random from the class.
Determine whether the event ‘the student studies physics’ and the event ‘the student studies geography’ are independent.
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(b)
[4]
It is known that for the whole college:
the probability of a student studying mathematics is 
the probability of a student studying biology is 
the probability of a student studying biology given that they study mathematics is 
Calculate the probability that a student studies mathematics or biology or both.
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