Dice and coin tosses – experimental probability
MathematicsProbabilityAges 11–12
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Probability
Roll a die or flip a coin many times; each outcome is tallied in a table and a frequency bar chart updates instantly. Students compare the experimental probability (number of times an outcome occurs divided by the total number of trials) with the theoretical probability of 1/6 or 1/2, and watch the two values converge as the number of trials grows.
Lesson: Experimental probability; frequency tables, bar charts
What it shows
Experimental probability is the relative frequency of an outcome: the number of times it occurs divided by the number of trials. For a fair six-sided die each face has theoretical probability 1/6, and for a fair coin each side has 1/2. The simulation tosses the chosen object repeatedly, fills a frequency table and draws a bar chart with an optional line at the expected count. With few trials the bars are uneven; as the number of trials grows, relative frequencies settle near the theoretical value, illustrating the law of large numbers.
How to use
Set the Number of trials and choose the Object to toss. Press Toss once a few times to see single outcomes being tallied, then press Run, adjusting the Toss speed to suit the class. Keep Show theoretical probability line on and compare the bars with it. Press Reset and repeat with 10 trials and then with 1000 trials, comparing the largest deviation reported under the chart.
Parameters you can change
- Number of trials 10–1000 trials
- Object to toss Six-sided die, Coin (H/T)
- Toss speed 1–100 trials/s
- Show theoretical probability line
Questions to explore
- In 60 rolls of a die, must the six appear exactly 10 times? What did you observe?
- Using a frequency table built from your bar chart, what is the experimental probability of each face?
- How does increasing the number of trials change the gap between experimental and theoretical probability?
