probability worksheet dice rolling

Dice Probability Worksheets

Dice probability worksheets Whether you’re wondering what your chances of success are in a game or are just preparing for an assignment or exam on probabilities, solving dice probabilities worksheet is a good starting point. Not only does it introduce you to the basics of calculating probabilities, it’s also directly relevant to craps and board games. It's easy to figure out the probabilities for dice, and you can build your knowledge from the basics to complex calculations in just a few steps.

Benefits of Dice Probability Worksheets

The simplest case when you're learning through dice probability worksheets is that the chance of getting a specific number with one die. The basic rule for probability is that you calculate it by looking at the number of possible outcomes in comparison to the outcome you’re interested in. So for a die, there are six faces, and for any roll, there are six possible outcomes. There is only one outcome you’re interested in, no matter which number you choose.

The formula you use is: Probability = Favourable Outcome / Total outcome .

Download Dice Probability Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

• Rolling Dice Probability Worksheet

Practice different types of rolling dice probability questions like probability of rolling a die, probability for rolling two dice simultaneously and probability for rolling three dice simultaneously in rolling dice probability worksheet.

1. A die is thrown 350 times and the score of 6 is obtained 28 times. Find the probability of 

(i) getting the score of 6 

(ii) getting a score under 6.

2. A die is rolled 500 times and the frequencies of the scores obtained are given below.

Find the probability of getting each score. Verify if their sum is 1.

3. Write down the total number of possible outcomes when the following experiment is done.

(i) A die is rolled

(ii) Two dices are rolled simultaneously.

4. A die is rolled at random. Write the number of favourable outcomes for the following events:

(i) getting a number less than 5

(ii) getting a prime number.

5. Two coins are tossed simultaneously. Write the number of favourable outcomes for the following events:

(i) getting at least one tail

(ii) getting tail

6. Fill in the blanks.

(i) A die is rolled at random. The probability of getting 2 is ....... .

(ii) A die is rolled at random. The probability of not getting 4 is ....... .

7. A die is rolled once. Find the probability of getting

(i) the number 5

(ii) an odd number

(iii) a number lying between 3 and 6

8. A die is rolled once. Find the probability that the number is

(ii) greater than 2

9. Two dice, one white and one red, are rolled together. Find the probability of getting

(i) a sum of 6

(ii) two different digits

(iii) a difference of 1.

Answers for the rolling dice probability worksheet are given below to check the exact answers of the above questions.

1.  (i) \(\frac{2}{25}\)

(ii) \(\frac{23}{25}\)

2.  \(\frac{3}{20}\), \(\frac{4}{25}\), \(\frac{17}{100}\), \(\frac{9}{50}\), \(\frac{21}{125}\), \(\frac{43}{250}\); Yes

3.  (i) 6

4.  (i) 4

5.  (i) 3

6.  (i) \(\frac{1}{6}\)

(ii) \(\frac{5}{6}\)

7.  (i) \(\frac{1}{6}\)

(ii) \(\frac{1}{2}\)

(iii) \(\frac{1}{3}\)

8.  (i) \(\frac{1}{2}\)

(ii) \(\frac{2}{3}\)

9.  (i) \(\frac{5}{36}\)

(iii) \(\frac{5}{18}\)

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Roll One Dice Die Random Investigation Theoretical Probability Experiment Resource Bundle Pack

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

1 June 2019

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All you need to have a lesson based on rolling one die and recording the outcomes.

I’ve done this activity as part of circus of many activities in a lesson (Other circus activities listed on my TES Resources pages) but you can make a whole lesson out of this depending on what you are trying to achieve.

Many different versions of the task sheets. Look at them all and decide on the best to suit your learners. Several different versions of Excel Spreadsheets to record the results on - including one which I can’t remember how it works (the RANDOM one).

If you find it useful please leave a helpful review.

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Probability Activity Investigation Bundle

A huge bundle of Probability resources for KS3 or Foundation GCSE. Individually they are either free or max £2. Combined total price is £14 before bundling so you are getting it for almost half price here. Many activities are game and investigation based to help understanding of principles and concepts. If you like please review and then check out my other resources in my shop.

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Dice Probability Worksheet

You could even simulate some of these problems with a class set of dice to let students estimate their answers, then let them calculate the probabilities when they have the necessary knowledge. Comparisons of the experimental results and the computational results is encouraged, and could be used to introduce the Law of Large Numbers.

Assume all problems involve traditional six-sided dice.

1. What is the probability of rolling a 2 in one dice roll?

(i) What is the probability of rolling at least one 2 in two dice rolls?

(ii) What is the probability of rolling exactly one 2 in two dice rolls?

3. What is the probability of rolling an odd number in one dice roll?

(i) What is the probability of rolling "doubles" (two of the same number) in two dice rolls?

(ii) What is the probability of rolling two or more dice with the same number in three rolls (this question is likely too difficult for a middle school class to answer; I recommend omitting it in this scenario).

5. In Monopoly, you are sent to the Jail space if you roll doubles three consecutive times. What is the probability of this happening in some set of three consecutive dice rolls?

6. Which is more likely: rolling a 5 on a standard die three times in a row, or flipping "heads" on a fair two-sided coin six times in a row?

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Probability with Dice

• The sample space is the list of all possible outcomes.
• A dice has 6 sides which are all equally likely to be rolled.
• Each side has a different number written on it.
• We can roll a: 1, 2, 3, 4, 5 or a 6.
• We say that the sample space for a dice is: 1, 2, 3, 4, 5, 6.
• Probability is a measure of the chance of something happening.
• We can write the probability of rolling a 3 as a fraction.
• There are 6 different outcomes in total that we can roll.
• So the fraction is out of 6.
• Only one side of the dice is a ‘3’.
• So the probability of rolling a three is   1 / 3   .
• The number three makes up 1 out of 6 sides of the dice and on average will be rolled once every six rolls.

• We will write the probability of rolling an odd number on a dice as a fraction.
• The odd numbers are 1, 3 and 5.
• This is 3 of the 6 sides of the dice.
• The probability of rolling an odd number on a dice is   3 / 6  .
•   3 / 6   is the same as   1 / 2  
• You can expect an odd number to be rolled half of the time.

• Shading Fractions of Shapes
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Dice Probability Worksheets and Answers

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Polymath: The Blog for Parents and Educators

What’s the most common result of rolling two dice? Printable worksheet included

February 05, 2022

Probability is one of our favourite mathematics concepts! Despite it being everywhere in the world around us, it can be hard to come up with interesting math problems.

Lessons around probability often start with dice rolling and coin flips. Dice rolling is great because it’s usually in a child’s life through board games. Lots of board games don’t have one dice, they have two!

This adds a little complexity to the problem. When we roll two dice and add the result, we can ask a bunch of questions, like:

• What are all the different numbers that can come up?
• What are the most common number(s)?
• What is the chance of the most common number(s) coming up?
• What are the least common number(s)?
• What is the chance of the least common number(s) coming up?

We’ve put together a printable worksheet that your child can work through on their own or with you. This post also has a detailed explanation on the problems in the worksheet. Click to download.

Problem 1: Performing an experiment

This is great for children who are just getting started with probability. It’s just about observation!

Break out a piece of paper and draw an x (horizontal) axis for a graph on it. On the axis write 1, 2, 3... all the way up to 12.

Then you and your child can roll two dice, add up the numbers, and record each sum. If you’re on paper with squares, you can colour in a square for each roll.

Do this for a while, it’ll take some time (around 50 rolls) before you see noticeable patterns. You could even do it over multiple days for 5 minutes a day.

After this is done, you may have something that looks like this:

We can’t make any guarantees as we’re dealing with randomness—that’s the whole point of probability and statistics. However, the trend should emerge that there are fewer rolls on the lowest and higher numbers, with a bump in the middle (around 6-8).

Here’s the interesting result: not all numbers have the same probability! Unlike rolling a single die, where each number has the same chance of coming up, rolling two die makes the distribution of results uneven. If you’re trying to make up your own dice games, this becomes important to keep in mind.

Problem 2. Working out the probabilities

In the experiment we determined that the numbers around the middle are the most likely. For more advanced children who understand probability as numbers (e.g. a coin flip has a 1 in 2 chance of coming up tails), we can work this out more precisely. According to probability theory, which is the most common number? Is there more than one of them?

We can work this out by calculating every single outcome of rolling two die. There are only 36 of them. Using a chart like this, we can calculate all of them. Here they are

Immediately we can see some patterns emerge. There are these diagonal strips of numbers going from the bottom left to the top right. I think you can see what the most common number is now. We can look at it a slightly different way, though, by putting it into the histogram from above.

What do you observe here? Here are some things we see:

• The shape is much neater than the experiment from before. In fact, it’s a perfect triangle!
• 7 is the most common result. How do we work out the probability of getting a 7? Well, we divide the number of times it comes up (6 times) by all the possible outcomes(36). So it’s a 6 in 36 chance. Or a 1 in 6 chance.
• 2 and 12 are the least common results. They each have a 1 in 36 chance of appearing.
• 1 is impossible to come up

That’s just the way the dice roll

This is a fun exercise in probability that’s a little more complex than the single dice roll. You can take it further, too. What do you think would happen with three dice? What happens when you multiply the numbers instead of adding them?

We’d love to hear about how you use this exercise, so let us know on email , Twitter , Facebook or Instagram .