🎲 Probability Experiment Simulators

Run interactive simulations to see frequentist probabilities in action. Compare empirical results with theoretical expectations for coins, dice, the birthday paradox, and the Monty Hall problem. Designed for quick classroom demos and intuition-building.

1. Coin Toss Simulator

Empirical probability of heads vs theoretical 50%.

Number of tosses

Results

Heads: —
Tails: —
Difference from 50%: —

2. Dice Roll Distribution

View frequency of sums for rolling dice multiple times.

Number of dice

Rolls per simulation

Frequency by outcome

—

3. Birthday Paradox Calculator

Probability of at least two people sharing a birthday.

People in room

Days per year

Probability of shared birthday

—

4. Monty Hall Simulation

Compare “stay” vs “switch” strategies.

Number of trials

Winning probability

Stay strategy: —
Switch strategy: —

Switching should approach 66.7% as trials increase.

How to Use

Select the simulation card you need, enter the number of trials or participants, and click the run button.
Observe empirical results alongside theoretical expectations; adjust the number of trials to see convergence behaviour.
Use the reset buttons where provided to clear previous outcomes before running a fresh configuration.
Interpret the live-region narration (for accessibility) to track outcomes when running multiple demos quickly.

References

Hamming, R. (1987). The Art of Probability for Scientists and Engineers. Addison-Wesley.
MIT OpenCourseWare. (2018). 6.041 Probabilistic Systems Analysis and Applied Probability – Simulation labs.