Standard Survey to Venn Diagram

Questions that provide survey data with counts for individual categories and overlaps (e.g., 'X like A', 'Y like both A and B') and require constructing a Venn diagram from these counts.

9 questions

Edexcel S1 2005 January Q5
5. Articles made on a lathe are subject to three kinds of defect, \(A , B\) or \(C\). A sample of 1000 articles was inspected and the following results were obtained. \begin{displayquote} 31 had a type \(A\) defect
37 had a type \(B\) defect
42 had a type \(C\) defect
11 had both type \(A\) and type \(B\) defects
13 had both type \(B\) and type \(C\) defects
10 had both type \(A\) and type \(C\) defects
6 had all three types of defect.
  1. Draw a Venn diagram to represent these data. \end{displayquote} Find the probability that a randomly selected article from this sample had
  2. no defects,
  3. no more than one of these defects. An article selected at random from this sample had only one defect.
  4. Find the probability that it was a type \(B\) defect. Two different articles were selected at random from this sample.
  5. Find the probability that both had type \(B\) defects.
Edexcel S1 2008 January Q5
5. The following shows the results of a wine tasting survey of 100 people. \begin{displayquote} 96 like wine \(A\),
93 like wine \(B\),
96 like wine \(C\),
92 like \(A\) and \(B\),
91 like \(B\) and \(C\),
93 like \(A\) and \(C\),
90 like all three wines.
  1. Draw a Venn Diagram to represent these data. \end{displayquote} Find the probability that a randomly selected person from the survey likes
  2. none of the three wines,
  3. wine \(A\) but not wine \(B\),
  4. any wine in the survey except wine \(C\),
  5. exactly two of the three kinds of wine. Given that a person from the survey likes wine \(A\),
  6. find the probability that the person likes wine \(C\).
Edexcel S1 2010 January Q4
4. There are 180 students at a college following a general course in computing. Students on this course can choose to take up to three extra options. \begin{displayquote} 112 take systems support,
70 take developing software,
81 take networking,
35 take developing software and systems support,
28 take networking and developing software,
40 take systems support and networking,
4 take all three extra options.
  1. In the space below, draw a Venn diagram to represent this information. \end{displayquote} A student from the course is chosen at random. Find the probability that this student takes
  2. none of the three extra options,
  3. networking only. Students who want to become technicians take systems support and networking. Given that a randomly chosen student wants to become a technician,
  4. find the probability that this student takes all three extra options.
Edexcel S1 2012 January Q6
  1. The following shows the results of a survey on the types of exercise taken by a group of 100 people.
65 run
48 swim
60 cycle
40 run and swim
30 swim and cycle
35 run and cycle
25 do all three
  1. Draw a Venn Diagram to represent these data. Find the probability that a randomly selected person from the survey
  2. takes none of these types of exercise,
  3. swims but does not run,
  4. takes at least two of these types of exercise. Jason is one of the above group.
    Given that Jason runs,
  5. find the probability that he swims but does not cycle.
Edexcel S1 2001 June Q5
5. A market researcher asked 100 adults which of the three newspapers \(A , B , C\) they read. The results showed that \(30 \operatorname { read } A , 26\) read \(B , 21\) read \(C , 5\) read both \(A\) and \(B , 7\) read both \(B\) and \(C , 6\) read both \(C\) and \(A\) and 2 read all three.
  1. Draw a Venn diagram to represent these data. One of the adults is then selected at random.
    Find the probability that she reads
  2. at least one of the newspapers,
  3. only \(A\),
  4. only one of the newspapers,
  5. \(A\) given that she reads only one newspaper.
Edexcel S1 2006 June Q6
  1. A group of 100 people produced the following information relating to three attributes. The attributes were wearing glasses, being left handed and having dark hair.
    Glasses were worn by 36 people, 28 were left handed and 36 had dark hair. There were 17 who wore glasses and were left handed, 19 who wore glasses and had dark hair and 15 who were left handed and had dark hair. Only 10 people wore glasses, were left handed and had dark hair.
    1. Represent these data on a Venn diagram.
    A person was selected at random from this group.
    Find the probability that this person
  2. wore glasses but was not left handed and did not have dark hair,
  3. did not wear glasses, was not left handed and did not have dark hair,
  4. had only two of the attributes,
  5. wore glasses given that they were left handed and had dark hair.
Edexcel S1 2015 June Q3
  1. A college has 80 students in Year 12.
20 students study Biology
28 students study Chemistry
30 students study Physics
7 students study both Biology and Chemistry
11 students study both Chemistry and Physics
5 students study both Physics and Biology
3 students study all 3 of these subjects
  1. Draw a Venn diagram to represent this information. A Year 12 student at the college is selected at random.
  2. Find the probability that the student studies Chemistry but not Biology or Physics.
  3. Find the probability that the student studies Chemistry or Physics or both. Given that the student studies Chemistry or Physics or both,
  4. find the probability that the student does not study Biology.
  5. Determine whether studying Biology and studying Chemistry are statistically independent.
SPS SPS SM Statistics 2021 September Q3
3. There are 180 students at a college following a general course in computing. Students on this course can choose to take up to three extra options. \begin{displayquote} 112 take systems support,
70 take developing software,
81 take networking,
35 take developing software and systems support,
28 take networking and developing software,
40 take systems support and networking,
4 take all three extra options. \end{displayquote} a Draw a Venn diagram to represent this information. A student from the course is chosen at random.
b Find the probability that this student takes
i none of the three extra options
ii networking only. Students who take systems support and networking are eligible to become technicians.
c Given that the randomly chosen student is eligible to become a technician, find the probability that this student takes all three extra options.
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AQA Paper 3 2022 June Q16
16 A sample of 240 households were asked which, if any, of the following animals they own as pets:
  • cats (C)
  • dogs (D)
  • tortoises ( \(T\) )
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
153704548213217
16
  1. Represent this information by fully completing the Venn diagram below.
    \includegraphics[max width=\textwidth, alt={}, center]{6ad3bac9-bf08-443d-8be2-b0c26209ffe8-24_858_1191_1032_427} 16
  2. A household is chosen at random from the sample.
    16
    1. Find the probability that the household owns a cat only. 16
  4. (ii) Find the probability that the household owns at least two of the three types of pet.
    16
  5. (iii) Find the probability that the household owns a cat or a dog or both, given that the household does not own a tortoise.
    16
  6. Determine whether a household owning a cat and a household owning a tortoise are independent of each other. Fully justify your answer.