Worksheets · Statistics

Venn diagram probability worksheet

Every region of a Venn diagram is a count. Or is everything inside either circle, and is the overlap, and given shrinks the whole to one circle.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Venn Diagrams

Date Period

Find each probability.

  1. The Venn diagram shows 41 students. A student is picked at random. Find P(Math and Art).MathArt2121215
  2. The Venn diagram shows 25 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess9268
  3. The Venn diagram shows 27 households. A household is picked at random. Find P(Dogs and Cats).DogsCats16371
  4. The Venn diagram shows 37 students. A student is picked at random. Find P(Math given Art).MathArt173710
  5. The Venn diagram shows 38 people. A person is picked at random. Find P(not Tea).TeaCoffee561512
  6. The Venn diagram shows 57 households. A household is picked at random. Find P(not Dogs).DogsCats14122011
  7. The Venn diagram shows 38 people. A person is picked at random. Find P(Tea and Coffee).TeaCoffee191414
  8. The Venn diagram shows 42 people. A person is picked at random. Find P(Tea given Coffee).TeaCoffee119193
  9. The Venn diagram shows 32 people. A person is picked at random. Find P(Tea or Coffee).TeaCoffee42206
  10. The Venn diagram shows 37 households. A household is picked at random. Find P(Dogs or Cats).DogsCats87148
  11. The Venn diagram shows 31 students. A student is picked at random. Find P(not Math).MathArt111064
  12. The Venn diagram shows 30 students. A student is picked at random. Find P(Math or Art).MathArt14565
  13. The Venn diagram shows 31 students. A student is picked at random. Find P(not Soccer).SoccerChess16393
  14. The Venn diagram shows 35 students. A student is picked at random. Find P(Soccer given Chess).SoccerChess15875
  15. The Venn diagram shows 48 households. A household is picked at random. Find P(Dogs given Cats).DogsCats14101410
  16. The Venn diagram shows 25 students. A student is picked at random. Find P(Soccer and Chess).SoccerChess10168
  17. The Venn diagram shows 43 students. A student is picked at random. Find P(Math given Art).MathArt1212910
  18. The Venn diagram shows 37 students. A student is picked at random. Find P(Math and Art).MathArt191251
  19. The Venn diagram shows 25 households. A household is picked at random. Find P(Dogs or Cats).DogsCats51163
  20. The Venn diagram shows 42 people. A person is picked at random. Find P(not Tea).TeaCoffee712176

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Venn DiagramsAnswer keyVersion 1

Date Period

Find each probability.

  1. The Venn diagram shows 41 students. A student is picked at random. Find P(Math and Art).MathArt21212151241
  2. The Venn diagram shows 25 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess92681725
  3. The Venn diagram shows 27 households. A household is picked at random. Find P(Dogs and Cats).DogsCats1637119
  4. The Venn diagram shows 37 students. A student is picked at random. Find P(Math given Art).MathArt173710310
  5. The Venn diagram shows 38 people. A person is picked at random. Find P(not Tea).TeaCoffee5615122738
  6. The Venn diagram shows 57 households. A household is picked at random. Find P(not Dogs).DogsCats141220113157
  7. The Venn diagram shows 38 people. A person is picked at random. Find P(Tea and Coffee).TeaCoffee191414138
  8. The Venn diagram shows 42 people. A person is picked at random. Find P(Tea given Coffee).TeaCoffee119193928
  9. The Venn diagram shows 32 people. A person is picked at random. Find P(Tea or Coffee).TeaCoffee422061316
  10. The Venn diagram shows 37 households. A household is picked at random. Find P(Dogs or Cats).DogsCats871482937
  11. The Venn diagram shows 31 students. A student is picked at random. Find P(not Math).MathArt1110641031
  12. The Venn diagram shows 30 students. A student is picked at random. Find P(Math or Art).MathArt1456556
  13. The Venn diagram shows 31 students. A student is picked at random. Find P(not Soccer).SoccerChess163931231
  14. The Venn diagram shows 35 students. A student is picked at random. Find P(Soccer given Chess).SoccerChess15875815
  15. The Venn diagram shows 48 households. A household is picked at random. Find P(Dogs given Cats).DogsCats14101410512
  16. The Venn diagram shows 25 students. A student is picked at random. Find P(Soccer and Chess).SoccerChess10168125
  17. The Venn diagram shows 43 students. A student is picked at random. Find P(Math given Art).MathArt121291047
  18. The Venn diagram shows 37 students. A student is picked at random. Find P(Math and Art).MathArt1912511237
  19. The Venn diagram shows 25 households. A household is picked at random. Find P(Dogs or Cats).DogsCats511632225
  20. The Venn diagram shows 42 people. A person is picked at random. Find P(not Tea).TeaCoffee7121762342

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

In a Venn diagram of 30 students, 12 are in A only, 5 are in both, 8 are in B only and 5 in neither. Find P(A or B).

  1. A or B is everyone inside either circle: 12 + 5 + 8 = 25.
  2. 25 out of 30.

The answer is 56.

Where students go wrong

Adding both circles in full for or, which counts the overlap twice.

Also called Venn diagram probability or union and intersection.

Questions about these worksheets

Yes. Every venn diagram probability sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the venn diagram probability questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Adding both circles in full for or, which counts the overlap twice.