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Quiz: Venn Diagram and Probability Review

10 questions

12th - 12th Grade

Mathematics

Quiz: Venn Diagram and Probability Review is a Grade 12 mathematics worksheet with 10 multiple-choice questions. The first two items ask students to interpret two-set survey information, distinguish overlap from “only” categories and the outside region, and select the correct Venn diagram labels. Students then identify probabilities for History, Science, their complements, the intersection of History and Science, the complement of that intersection, the union of History or Science, and the complement of the union. This worksheet strengthens students’ ability to translate set relationships into probability notation, including P(H), P(S), complements, intersections, and unions. Its repeated multiple-choice format provides focused practice with recognizing which region or event a notation describes and checking whether a selected probability expression matches the stated relationship. It is a free printable worksheet with a complete answer key, suitable for review, independent practice, or a short assessment after instruction on Venn diagrams and event notation.

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Quiz: Venn Diagram and Probability Review

Total questions: 10

Name
Class
Date
1.

Ms. Stringer conducted a survey of his 9th grader homeroom.  17 students are taking both Econ and Business.  19 students are only taking Econ.  18 students are only taking Business.  16 students are taking other courses.

Construct Venn Diagram. Which one of the followings is correct for the given Venn picture.

a)

i = 16, ii = 17, iii = 18. iv = 19

b)

i = 19, ii = 18, iii = 17. iv = 16

c)

i = 19, ii = 17, iii = 18. iv = 16

d)

i = 16, ii = 18, iii = 17. iv = 19

2.

Mr. Jones conducted a survey of his 9th grader homeroom.  20 students are taking both Econ and Business.  30 students are taking Econ (subtract to 20).  15 students are only taking Business.  25 students are taking other courses.

Construct Venn Diagram. Which one of the followings is correct for the given Venn picture.

a)

i = 10, ii = 15, iii = 20. iv = 25

b)

i = 25, ii = 20, iii = 15. iv = 10

c)

i = 15, ii = 20, iii = 25. iv = 30

d)

i = 30, ii = 25, iii = 20. iv = 15

3.

Determine the probability of History

a)

P(H) =

3 +521\frac{3\ +5}{21}  

b)

P(H) =

4 +521\frac{4\ +5}{21}  

c)

P(H) =

3 +921\frac{3\ +9}{21}  

d)

P(H) =

4 +921\frac{4\ +9}{21}  

4.

Determine the probability of History Complement

a)

P(H)' =

3 +521\frac{3\ +5}{21}  

b)

P(H)' =

4 +521\frac{4\ +5}{21}  

c)

P(H)' =

3 +921\frac{3\ +9}{21}  

d)

P(H)' =

4 +921\frac{4\ +9}{21}  

5.

Determine the probability of Science

a)

P(S) =

3 +521\frac{3\ +5}{21}  

b)

P(S) =

4 +521\frac{4\ +5}{21}  

c)

P(S) =

3 +921\frac{3\ +9}{21}  

d)

P(S) =

4 +921\frac{4\ +9}{21}  

6.

Determine the probability of Science Complement

a)

P(S)' =

3 +521\frac{3\ +5}{21}  

b)

P(S)' =

4 +521\frac{4\ +5}{21}  

c)

P(S)' =

3 +921\frac{3\ +9}{21}  

d)

P(S)' =

4 +921\frac{4\ +9}{21}  

7.

Determine the probability of History and/intersection Science

denoted P(H ∩\cap  S)

a)

P(H and S) =

3 21\frac{3\ }{21}  

b)

P(H and S) =

4 21\frac{4\ }{21}  

c)

P(H and S) =

3 +5+921\frac{3\ +5+9}{21}  

d)

P(H and S) =

4 +5+921\frac{4\ +5+9}{21}  

8.

Determine the probability of History and/intersection Science Complement

denoted P(H ∩\cap  S)'

a)

P(H and S)' =

3 21\frac{3\ }{21}  

b)

P(H and S)' =

4 21\frac{4\ }{21}  

c)

P(H and S)' =

3 +5+921\frac{3\ +5+9}{21}  

d)

P(H and S)' =

4 +5+921\frac{4\ +5+9}{21}  

9.

Determine the probability of History or/uninon Science

denoted P(H ∪\cup  S)

a)

P(H or S) =

3 21\frac{3\ }{21}  

b)

P(H or S) =

4 21\frac{4\ }{21}  

c)

P(H or S) =

3 +5+921\frac{3\ +5+9}{21}  

d)

P(H or S) =

4 +5+921\frac{4\ +5+9}{21}  

10.

Determine the probability of History or/union Science Complement

denoted P(H ∪\cup  S)'

a)

P(H or S)' =

3 21\frac{3\ }{21}  

b)

P(H or S)' =

4 21\frac{4\ }{21}  

c)

P(H or S)' =

3 +5+921\frac{3\ +5+9}{21}  

d)

P(H or S)' =

4 +5+921\frac{4\ +5+9}{21}  

Answer Key

Quiz: Venn Diagram and Probability Review

Total questions: 10

1.
b)

i = 19, ii = 18, iii = 17. iv = 16

2.
a)

i = 10, ii = 15, iii = 20. iv = 25

3.
c)

P(H) =

3 +921\frac{3\ +9}{21}  

4.
b)

P(H)' =

4 +521\frac{4\ +5}{21}  

5.
a)

P(S) =

3 +521\frac{3\ +5}{21}  

6.
d)

P(S)' =

4 +921\frac{4\ +9}{21}  

7.
a)

P(H and S) =

3 21\frac{3\ }{21}  

8.
d)

P(H and S)' =

4 +5+921\frac{4\ +5+9}{21}  

9.
c)

P(H or S) =

3 +5+921\frac{3\ +5+9}{21}  

10.
b)

P(H or S)' =

4 21\frac{4\ }{21}  

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FAQs

What does the Venn Diagram and Probability Review worksheet cover?

This Grade 12 worksheet uses 10 multiple-choice questions to practise two connected skills: assigning survey counts to the correct regions of two-set Venn diagrams and identifying probabilities for events involving History and Science. Students work with single events, complements, intersections, unions, and complements of intersections or unions, building accuracy in translating set relationships into probability notation.

How can I use this worksheet to teach Venn diagrams and probability notation?

Begin by modelling how an overlap, an “only” category, and the outside region are placed in a two-set Venn diagram, then have students explain why the total Econ count in the second survey must be separated into the overlap and Econ-only region. After reviewing those diagrams, use the History and Science items to ask students to point to the event represented by each notation before selecting an answer. This sequence links visual regions to complements, intersections, and unions.

What mistakes should I watch for when students complete this worksheet?

Watch for students treating a total category count as an “only” count, failing to subtract the overlap, or placing the outside-course group inside one of the circles. In the probability items, students may confuse an intersection (“and”) with a union (“or”), or read a complement as the original event rather than everything outside it. These errors are especially visible in the paired questions for an event and its complement.

How do I assign and grade this Venn diagram and probability worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key for the two Venn diagram interpretation items and the probability-notation questions, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also supports schools that want to reduce screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the Venn diagram scenarios and probability notation are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language, depending on students’ needs.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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