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.

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 44 students. A student is picked at random. Find P(Math and Art).MathArt1512107
  3. The Venn diagram shows 25 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess9268
  4. The Venn diagram shows 27 households. A household is picked at random. Find P(Dogs and Cats).DogsCats16371
  5. The Venn diagram shows 37 students. A student is picked at random. Find P(Math given Art).MathArt173710
  6. The Venn diagram shows 38 people. A person is picked at random. Find P(not Tea).TeaCoffee561512
  7. The Venn diagram shows 31 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess16447
  8. The Venn diagram shows 33 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess152124
  9. The Venn diagram shows 47 students. A student is picked at random. Find P(Math and Art).MathArt1812611
  10. The Venn diagram shows 57 households. A household is picked at random. Find P(not Dogs).DogsCats14122011
  11. The Venn diagram shows 38 people. A person is picked at random. Find P(Tea and Coffee).TeaCoffee191414
  12. The Venn diagram shows 42 people. A person is picked at random. Find P(Tea given Coffee).TeaCoffee119193
  13. The Venn diagram shows 32 people. A person is picked at random. Find P(Tea or Coffee).TeaCoffee42206
  14. The Venn diagram shows 37 households. A household is picked at random. Find P(Dogs or Cats).DogsCats87148
  15. The Venn diagram shows 32 people. A person is picked at random. Find P(not Tea).TeaCoffee18275
  16. The Venn diagram shows 30 households. A household is picked at random. Find P(Dogs or Cats).DogsCats47145
  17. The Venn diagram shows 29 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess39710
  18. The Venn diagram shows 31 students. A student is picked at random. Find P(not Math).MathArt111064
  19. The Venn diagram shows 24 people. A person is picked at random. Find P(not Tea).TeaCoffee18321
  20. The Venn diagram shows 39 households. A household is picked at random. Find P(not Dogs).DogsCats152184

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 44 students. A student is picked at random. Find P(Math and Art).MathArt1512107311
  3. The Venn diagram shows 25 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess92681725
  4. The Venn diagram shows 27 households. A household is picked at random. Find P(Dogs and Cats).DogsCats1637119
  5. The Venn diagram shows 37 students. A student is picked at random. Find P(Math given Art).MathArt173710310
  6. The Venn diagram shows 38 people. A person is picked at random. Find P(not Tea).TeaCoffee5615122738
  7. The Venn diagram shows 31 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess164472431
  8. The Venn diagram shows 33 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess1521242933
  9. The Venn diagram shows 47 students. A student is picked at random. Find P(Math and Art).MathArt18126111247
  10. The Venn diagram shows 57 households. A household is picked at random. Find P(not Dogs).DogsCats141220113157
  11. The Venn diagram shows 38 people. A person is picked at random. Find P(Tea and Coffee).TeaCoffee191414138
  12. The Venn diagram shows 42 people. A person is picked at random. Find P(Tea given Coffee).TeaCoffee119193928
  13. The Venn diagram shows 32 people. A person is picked at random. Find P(Tea or Coffee).TeaCoffee422061316
  14. The Venn diagram shows 37 households. A household is picked at random. Find P(Dogs or Cats).DogsCats871482937
  15. The Venn diagram shows 32 people. A person is picked at random. Find P(not Tea).TeaCoffee1827538
  16. The Venn diagram shows 30 households. A household is picked at random. Find P(Dogs or Cats).DogsCats4714556
  17. The Venn diagram shows 29 students. A student is picked at random. Find P(Soccer or Chess).SoccerChess397101929
  18. The Venn diagram shows 31 students. A student is picked at random. Find P(not Math).MathArt1110641031
  19. The Venn diagram shows 24 people. A person is picked at random. Find P(not Tea).TeaCoffee1832118
  20. The Venn diagram shows 39 households. A household is picked at random. Find P(not Dogs).DogsCats1521842239

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.