Dice Probability Mastery Practice Test Worksheets
Probability questions involving dice are a staple of logic and maths tests. Once you understand the relationship between the number of sides and the target outcome, these questions become quick and easy marks.
For students who understand chance, but make mistakes counting favourable outcomes on dice with different numbers of sides.
Opens in Etsy, which handles checkouts and downloads.
What Do Dice Probability Questions Look Like?
Dice probability questions test your ability to determine the likelihood of single and combined outcomes on standard 6-sided dice. Success requires counting favourable outcomes accurately and simplifying fractions. Here is a worked example.
Simple Probability
Question: You roll a fair 6-sided die numbered 1 to 6. What is the probability of rolling a number less than 2?
Worked Method
What it's testing: Basic probability definition.
How to solve it: The only number less than 2 is 1, so there is 1 favourable outcome. There are 6 equally likely outcomes in total.
Probability = 16
Tip: "Fair" means every side has an equal chance of landing face up.
Rules to Help You Solve Dice Probability Questions
To solve dice probability questions like the example above, keep the sample space and outcome rules clear. Follow these four rules:
🎲 Rule 1: The Total Outcomes
For one roll of a die numbered this way, each face gives a different result, so the total number of outcomes equals the number of sides. A 10-sided die has 10 possible results.
Example: A 12-sided dice has 12 possible outcomes.
🎯 Rule 2: Successful Outcomes
Count how many of those sides match your condition (e.g., "odd", "greater than 5", "less than 3").
Example: On a 6-sided dice, "Greater than 4" means 5 and 6. That's 2 outcomes.
➗ Rule 3: The Probability Formula
When all outcomes are equally likely, probability = Favourable Outcomes ÷ Total Outcomes. Simplify your fraction if possible.
Example: 5 successes on a 10-sided dice = 510 = 12
⚖️ Rule 4: Certainty vs Impossibility
If an event is guaranteed (like rolling a number from 1-6 on a 6-sided dice), the probability is 1. If it's impossible, the probability is 0.
Example: Rolling a 7 on a 6-sided dice = 0
Two More Worked Examples
Here are two more examples showing how to work with outcome ranges and avoid certainty traps.
Range of Outcomes
Question: A fair die has 12 sides, numbered 1 to 12. What is the probability of rolling a number greater than 8?
Worked Method
What it's testing: Identifying a set of successful outcomes.
Step 1 — Identify successful outcomes: Numbers greater than 8 are 9, 10, 11, and 12. That is 4 outcomes.
Step 2 — Apply formula: 412
Step 3 — Simplify: 412 = 13
Tip: Be careful with the word "greater than" — it doesn't include the number itself.
Absolute Certainty
Question: A fair 6-sided die is numbered 1 to 6. What is the probability of rolling a number from the set 1, 2, 3, 4, 5, or 6?
Worked Method
Step 1 — Count favourable outcomes: The set includes all six numbers on the die.
Step 2 — Apply the formula: There are 6 favourable outcomes out of 6 equally likely outcomes. Probability = 66 = 1.
Tip: Probability 1 means certainty: every possible outcome satisfies the condition. It does not mean there is only one favourable outcome; one favourable face on this die would give probability 16.
