Our family has always enjoyed playing dice games. We love games with tons of dice, including games that use strange dice like D20s and D3s (which are some of my favorite dice because they are little triangles). For this Venn diagram **dice probability** STEM activity, I allowed Monkey to come up with her own formulas for the probability of certain numbers rolled on D20 dice.

Add these math challenges to your list of fun math activities for kids!

## Probability Lesson

We used three different lessons on probability before Monkey started her STEM experiment.

Dice probability and D6s

Venn Diagram probability using playing cards

What we did not find, however, is whether the rules would change using D20 dice or if they would stay the same. This is where our STEM activity came into play.

**Armed with all the knowledge technology could give us, we started our dice probability experiment.**

## Venn Diagram Dice Probability STEM Activity

**We used each of the four STEM topics in the following ways during our activity:**

**Science:** Monkey had a question and we sought to answer it through experimentation and by recording the data of our results. She created a hypothesis (that the probability laws would not change) and tested it.

**Technology:** Monkey used online resources to learn about dice probability and Venn diagrams.

**Engineering:** Monkey had to create her own test board and set of rules for her project.

**Math:** Monkey had to use math to find the answers to her questions.

*Note: Monkey came up with these formulas and calculations on her own. They may not be entirely correct mathematically, but she used her current math knowledge to come up with her answers, which helped expand her critical thinking, even if she didn’t get the correct answer. If you have more knowledge on dice probability, feel free to share it with us!*

*This post contains affiliate links for your convenience. *

### Supplies

- D20 dice (at least four)
- Marker
- Paper
- We also used our clay manupulatives, but that is optional

## Venn Diagram Dice Probability Test

First, Monkey wrote down the odds of rolling one number on a single die (1/20) then what those same odds were of rolling that number on four die (4/80). The odds remained the same at 1/20 no matter the number of die.

Next, she used the Venn Diagram to calculate what the probability of four dice rolling the same two numbers (10 and 13) would be. She calculated that the odds would be 1 in 40.

She rolled the dice 100 times and counted how many times the dice red both 10 and 13 in the same roll. In 100 rolls, she rolled the correct numbers three times, which fit in with her original calculations. However, she was surprised that she rolled the desired numbers twice within 24 rolls, but didn’t roll the third match until roll 97.

We discussed how just because something is probable, or likely to happen a certain way doesn’t mean it will happen exactly in the predicted manner (like precisely rolling the correct numbers once every 40 rolls). We discussed how variables like the person rolling the die, differences in dice weight, the speed and the size of the die might alter the actual results of a probability experiment.