Probability with Dice
To compare experimental probability with theoretical probability using dice rolls
Theory & Background
Theoretical probability predicts outcomes based on mathematical calculations, while experimental probability is based on actual trials. With more trials, experimental results should approach theoretical predictions due to the Law of Large Numbers.
Required Materials
- 2 standard six-sided dice
- Recording sheets
- Calculator
- Graphing materials
- Computer/tablet for data entry (optional)
Estimated Time
1-2 hours
Step-By-Step Procedure
Calculate theoretical probabilities for dice sums (2-12) using mathematical formulas.
Roll two dice 100 times and record the sum of each roll.
Create a frequency table showing how often each sum occurred.
Calculate experimental probabilities by dividing frequency by total rolls.
Compare experimental results to theoretical predictions.
Repeat with 200 rolls and then 300 rolls to see how results change.
Graph both theoretical and experimental probabilities to visualize differences.
⚠️ Experiment Tips
- Keep careful records of each roll to avoid counting errors.
- Try to eliminate bias by rolling dice consistently.
- Consider factors that might affect randomness.
- Compare results with other students to see variation.
Observation
With small numbers of rolls, experimental results often differ significantly from theoretical predictions. As the number of trials increases, experimental results usually get closer to theoretical values.
Result & Conclusion
The Law of Large Numbers demonstrates that experimental probability approaches theoretical probability as sample size increases. This principle underlies statistical analysis and quality control in many industries.