Worksheets · Algebra 2

Independent and dependent events worksheet

Two things happening means multiplying their chances. The only question is whether the first one changed the second: put the marble back and it did not, keep it and it did.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Independent and Dependent Events

Date Period

Find each probability.

  1. A bag has 14 red and 8 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  2. A bag has 13 red and 18 blue counters. Two are drawn without replacement. Find P(both red).
  3. A bag has 18 red and 11 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  4. A bag has 14 red and 15 blue counters. Two are drawn without replacement. Find P(both red).
  5. A bag has 12 red and 18 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  6. A bag has 13 red and 13 blue counters. Two are drawn without replacement. Find P(both red).
  7. A bag has 9 red and 12 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  8. A bag has 10 red and 9 blue counters. Two are drawn without replacement. Find P(both red).
  9. A bag has 13 red and 8 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  10. A bag has 12 red and 16 blue counters. Two are drawn without replacement. Find P(both red).
  11. A bag has 11 red and 10 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  12. A bag has 8 red and 12 blue counters. Two are drawn without replacement. Find P(both red).
  13. A bag has 14 red and 16 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  14. A bag has 11 red and 10 blue counters. Two are drawn without replacement. Find P(both red).
  15. A bag has 15 red and 14 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  16. A bag has 16 red and 10 blue counters. Two are drawn without replacement. Find P(both red).
  17. A bag has 15 red and 12 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  18. A bag has 16 red and 18 blue counters. Two are drawn without replacement. Find P(both red).
  19. A bag has 10 red and 16 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).
  20. A bag has 9 red and 11 blue counters. Two are drawn without replacement. Find P(both red).

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

Sigma Prep · sigmaprep.io/worksheets

Name

Independent and Dependent EventsAnswer keyVersion 1

Date Period

Find each probability.

  1. A bag has 14 red and 8 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).49121
  2. A bag has 13 red and 18 blue counters. Two are drawn without replacement. Find P(both red).26155
  3. A bag has 18 red and 11 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).324841
  4. A bag has 14 red and 15 blue counters. Two are drawn without replacement. Find P(both red).1358
  5. A bag has 12 red and 18 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).425
  6. A bag has 13 red and 13 blue counters. Two are drawn without replacement. Find P(both red).625
  7. A bag has 9 red and 12 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).949
  8. A bag has 10 red and 9 blue counters. Two are drawn without replacement. Find P(both red).519
  9. A bag has 13 red and 8 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).169441
  10. A bag has 12 red and 16 blue counters. Two are drawn without replacement. Find P(both red).1163
  11. A bag has 11 red and 10 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).121441
  12. A bag has 8 red and 12 blue counters. Two are drawn without replacement. Find P(both red).1495
  13. A bag has 14 red and 16 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).49225
  14. A bag has 11 red and 10 blue counters. Two are drawn without replacement. Find P(both red).1142
  15. A bag has 15 red and 14 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).225841
  16. A bag has 16 red and 10 blue counters. Two are drawn without replacement. Find P(both red).2465
  17. A bag has 15 red and 12 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).2581
  18. A bag has 16 red and 18 blue counters. Two are drawn without replacement. Find P(both red).40187
  19. A bag has 10 red and 16 blue counters. One is drawn, replaced, then another is drawn. Find P(both red).25169
  20. A bag has 9 red and 11 blue counters. Two are drawn without replacement. Find P(both red).1895

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

How to do these

2 red of 5, two drawn without replacement

  1. The first is 2 out of 5.
  2. Now only 1 red is left of 4.
  3. Multiply the two.

The answer is 110.

Where students go wrong

Keeping the same denominator on the second draw. Without replacement there is one fewer of everything, and using the original total is what makes a dependent question come out as an independent one.

Also called with and without replacement, compound probability or multiplying probabilities.

What you can put on this worksheet

Independent events: both the same
A bag has 4 red and 4 blue counters. One is drawn, replaced, then another is drawn. Find P(both red). → 14
Independent events: one of each
A bag has 4 red and 4 blue counters. One is drawn, replaced, then another is drawn. Find P(one of each color). → 12
Dependent events: both the same
A bag has 4 red and 4 blue counters. Two are drawn without replacement. Find P(both red). → 314
Dependent events: one of each
A bag has 4 red and 4 blue counters. Two are drawn without replacement. Find P(one of each color). → 47

Questions about these worksheets

Yes. Every independent and dependent events 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.

Algebra 2 is usually taken around 10th or 11th 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 independent and dependent events 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.

You pick from 4: independent events: both the same, independent events: one of each, dependent events: both the same and dependent events: one of each. Tick as many as you want and set how many of each, or let it spread them evenly.

Keeping the same denominator on the second draw. Without replacement there is one fewer of everything, and using the original total is what makes a dependent question come out as an independent one.