Worksheets · Statistics

Mutually exclusive events worksheet for Statistics

In Statistics the addition rule P(A or B) = P(A) + P(B) - P(A and B) is the main tool, and mutually exclusive is the special case where the last term is zero. The questions use cards, dice and given probabilities, and some ask you to decide from the numbers alone whether two events overlap.

Also taught in Algebra 2 and Precalculus, each at its own level and with its own examples.

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Name

Mutually Exclusive Events

Date Period

Find each probability, or answer as asked.

  1. Find P(A or B)P(A \text{ or } B)

    An 8-sided die is rolled. Find P(prime or greater than 4).
  2. An 8-sided die is rolled. Find P(a multiple of 3 or less than 3).
  3. A 6-sided die is rolled. Find P(even or less than 3).
  4. An 8-sided die is rolled. Find P(even or less than 6).
  5. An 8-sided die is rolled. Find P(even or greater than 5).
  6. A 6-sided die is rolled. Find P(less than 5 or a multiple of 3).
  7. A 6-sided die is rolled. Find P(less than 3 or greater than 3).

  1. Decide if the events are mutually exclusive

    One card is drawn from a standard deck. Are drawing a number card (2 to 10) and drawing a diamond mutually exclusive?
  2. One card is drawn from a standard deck. Are drawing a queen and drawing a red card mutually exclusive?
  3. One card is drawn from a standard deck. Are drawing a queen and drawing a king mutually exclusive?
  4. One card is drawn from a standard deck. Are drawing a spade and drawing an ace mutually exclusive?
  5. One card is drawn from a standard deck. Are drawing a red card and drawing a spade mutually exclusive?
  6. One card is drawn from a standard deck. Are drawing a king and drawing a red card mutually exclusive?
  7. One card is drawn from a standard deck. Are drawing a black card and drawing a diamond mutually exclusive?

  1. Find P(A or B)P(A \text{ or } B) for overlapping events

    P(A)=0.4, P(B)=0.6, and P(A and B)=0.05. Find P(A or B).
  2. One card is drawn from a standard deck. Find P(an ace or a spade).
  3. One card is drawn from a standard deck. Find P(a black card or a king).
  4. One card is drawn from a standard deck. Find P(a number card (2 to 10) or a heart).
  5. One card is drawn from a standard deck. Find P(a face card or a spade).
  6. P(A)=0.6, P(B)=0.6, and P(A and B)=0.2. Find P(A or B).

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

Sigma Prep · sigmaprep.io/worksheets

Name

Mutually Exclusive EventsAnswer keyVersion 2

Date Period

Find each probability, or answer as asked.

  1. Find P(A or B)P(A \text{ or } B)

    An 8-sided die is rolled. Find P(prime or greater than 4).34
  2. An 8-sided die is rolled. Find P(a multiple of 3 or less than 3).12
  3. A 6-sided die is rolled. Find P(even or less than 3).23
  4. An 8-sided die is rolled. Find P(even or less than 6).78
  5. An 8-sided die is rolled. Find P(even or greater than 5).58
  6. A 6-sided die is rolled. Find P(less than 5 or a multiple of 3).56
  7. A 6-sided die is rolled. Find P(less than 3 or greater than 3).56

  1. Decide if the events are mutually exclusive

    One card is drawn from a standard deck. Are drawing a number card (2 to 10) and drawing a diamond mutually exclusive?No
  2. One card is drawn from a standard deck. Are drawing a queen and drawing a red card mutually exclusive?No
  3. One card is drawn from a standard deck. Are drawing a queen and drawing a king mutually exclusive?Yes
  4. One card is drawn from a standard deck. Are drawing a spade and drawing an ace mutually exclusive?No
  5. One card is drawn from a standard deck. Are drawing a red card and drawing a spade mutually exclusive?Yes
  6. One card is drawn from a standard deck. Are drawing a king and drawing a red card mutually exclusive?No
  7. One card is drawn from a standard deck. Are drawing a black card and drawing a diamond mutually exclusive?Yes

  1. Find P(A or B)P(A \text{ or } B) for overlapping events

    P(A)=0.4, P(B)=0.6, and P(A and B)=0.05. Find P(A or B).0.95
  2. One card is drawn from a standard deck. Find P(an ace or a spade).413
  3. One card is drawn from a standard deck. Find P(a black card or a king).713
  4. One card is drawn from a standard deck. Find P(a number card (2 to 10) or a heart).1013
  5. One card is drawn from a standard deck. Find P(a face card or a spade).1126
  6. P(A)=0.6, P(B)=0.6, and P(A and B)=0.2. Find P(A or B).1

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

How to do these

One card is drawn from a standard deck. Find P(a heart or a queen)

  1. There are 13 hearts and 4 queens, and the queen of hearts is in both.
  2. Cards that count: 13 + 4 - 1 = 16.
  3. P = 16/52.

The answer is 413.

Where students go wrong

Calling two events mutually exclusive because they sound different. A red card and a king can be the same card, the king of hearts, so check whether any single outcome belongs to both before dropping the overlap.

Also called probability of A or B, addition rule or overlapping events.

What you can put on this worksheet

One event or the other
A 6-sided die is rolled. Find P(greater than 3 or less than 3). → 56
Mutually exclusive or not?
A die is rolled. Are rolling a number less than 3 and rolling a prime number mutually exclusive? → No
Overlapping events
One card is drawn from a standard deck. Find P(a black card or a king). → 713
Or, when each item has a color and a number
A box has 9 dark chocolates, 1 of them with nuts, and 10 milk chocolates, 5 of them with nuts. One is picked at random. Find P(milk or with nuts). → 1119
Mutually exclusive? From the numbers
P(A)=0.4, P(B)=0.4, and P(A and B)=0.05. Are A and B mutually exclusive? → No: P(A and B)≠0
Find the missing probability with the addition rule
A and B are mutually exclusive. P(A)=0.4 and P(A or B)=0.8. Find P(B) → 0.4

Questions about these worksheets

Yes. Every mutually exclusive 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.

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 mutually exclusive 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 6: one event or the other, mutually exclusive or not?, overlapping events, or, when each item has a color and a number, mutually exclusive? from the numbers and find the missing probability with the addition rule. Tick as many as you want and set how many of each, or let it spread them evenly.

Adding without taking the overlap off. If both can happen at once, straight addition counts that case twice and the answer can even come out above 1, which is a signal something has gone wrong.