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Top 11 Probability Exercises for Students (with Free Printable PDF)

A downloadable PDF worksheet being filled out by a student

Whether you’re a math teacher, homeschooling parent, student, or education enthusiast, probability is a fun and foundational topic that helps students explore logic, data, and chance. Using simple tools like dice, coins, and spinners, you can introduce a wide range of mathematical concepts in an engaging, interactive way.

This guide offers 11 hands-on probability exercises that are ideal for use with FreeOnlineDiceRoller.com. Each activity lists a recommended grade range and offers tips for scaling the difficulty. Whether you’re teaching dice roll probability, exploring random outcomes, or running a simulation, these exercises are sure to roll up the fun and boost learning outcomes.

1. Roll and Record (Grades 4–6)

Objective: Introduce the idea of randomness and frequency.

Instructions:

  • Use a D6 (six-sided die)

  • Roll 30 times, record each result

  • Create a frequency table

Extension: Convert the frequency into fractions and percentages.

Make it easier: Use fewer rolls and focus only on counting occurrences.

Make it harder: Compare student results to theoretical probability.

Downloadable PDF: Worksheet_1_Roll_and_Record

2. Predict the Outcome (Grades 5–7)

Objective: Compare predictions with experimental results.

Instructions:

  • Ask students to predict how often each number will occur in 60 rolls

  • Roll using FreeOnlineDiceRoller.com

  • Compare predictions to actual outcomes

Make it easier: Reduce roll count and guide prediction with theoretical probability.

Make it harder: Discuss sample size and variance.

Downloadable PDF: Worksheet_2_Predict_the_Outcome

3. Two Dice, One Sum (Grades 6–8)

Objective: Explore compound outcomes.

Instructions:

  • Roll two D6s simultaneously

  • Record sum of both dice for 100 rolls

  • Create a histogram of the results

Why it works: Students see that some sums (like 7) appear more frequently.

Make it easier: Focus only on identifying highest/lowest frequency.

Make it harder: Calculate theoretical probabilities using combinations.

Downloadable PDF: Worksheet_3_Two_Dice_One_Sum

4. Dice Graph Challenge (Grades 6–8)

Objective: Turn data into visual insight.

Instructions:

  • Roll a D8 or D10 50 times

  • Record frequency and create a bar graph

Make it easier: Pre-draw the graph axes.

Make it harder: Graph using digital tools like Excel or Google Sheets.

Downloadable PDF: Worksheet_4_Dice_Graph_Challenge

5. Game of Risk (Grades 7–9)

Objective: Introduce expected value and strategic decision-making.

Scenario: Rolling a 1 ends your turn. Rolling 2-6 lets you move forward 1 space. Students must decide whether to risk another roll.

Instructions:

  • Simulate 50 turns

  • Record total moves per strategy

  • Analyze outcomes

Make it easier: Provide move tracking sheets.

Make it harder: Allow different rules (e.g., roll a D20).

Downloadable PDF: Worksheet_5_Game_of_Risk

6. Fair vs. Unfair Dice (Grades 7–10)

Objective: Explore ethics and probability.

Instructions:

  • Use a “loaded” die (pre-set outcomes) or simulate using biased values

  • Compare outcomes vs. fair die

Discussion: What makes a game fair?

Make it easier: Provide data samples.

Make it harder: Introduce weighted probability.

Downloadable PDF: Worksheet_6_Fair_vs_Unfair_Dice

7. Custom Dice Lab (Grades 8–10)

Objective: Experiment with probability design.

Instructions:

  • Design a custom six-sided die (not 1-6)

  • Roll and compare to standard die

Make it easier: Pre-select outcomes

Make it harder: Add point values to faces

Downloadable PDF: Worksheet_7_Custom_Dice_Lab

8. Probability Word Problems (Grades 6–9)

Objective: Apply probability to real-world logic problems.

Example Problem: “You roll two dice. What is the chance both land on even numbers?”

Make it easier: Use single-die problems.

Make it harder: Use combinations and conditional probability.

Downloadable PDF: Worksheet_8_Probability_Word_Problems

9. Experimental vs. Theoretical (Grades 6–9)

Objective: Compare expected outcomes to real results.

Instructions:

  • Calculate expected frequencies for D6

  • Roll 100 times

  • Compare and analyze differences

Make it easier: Roll fewer times.

Make it harder: Calculate standard deviation.

Downloadable PDF: Worksheet_9_Experimental_vs_Theoretical

10. Dice Probability Game Design (Grades 9–12)

Objective: Use probability to design a game.

Instructions:

  • Create a board game or RPG mechanic using dice

  • Include win conditions, scoring, and probability balancing

Make it easier: Use templates or examples.

Make it harder: Present to the class or write a probability justification.

Downloadable PDF: Worksheet_10_Dice_Probability_Game_Design

11. Strategic Rolling (Grades 9–12)

Objective: Learn probability trees and outcomes.

Scenario: Students choose how many dice to roll. If they roll at least one 6, they win.

Instructions:

  • Create a probability tree for 1, 2, and 3 dice

  • Determine best strategy

Make it easier: Use visuals and only 2 options.

Make it harder: Add more conditions or use D10s.

Downloadable PDF: Worksheet_11_Strategic_Rolling

Closing Thoughts

Teaching probability doesn’t require fancy tools or expensive curriculum. With nothing more than paper and a good online dice roller, you can bring rich mathematical concepts to life. These exercises are more than just fun classroom activities—they’re a gateway into logic, decision-making, and real-world thinking.

And be sure to explore other resources, games, and tools on FreeOnlineDiceRoller.com to roll your way to math mastery!