Choose among coin flips with custom p(Heads), weighted six-sided dice, or European/American roulette bets. The simulator compares theory and empirical ratios, shows Wilson 95% confidence intervals for binary outcomes, tracks running convergence, and records the exact steps it takes so you can explain them back to the class.
Need extra documentation? Use the CSV export for raw counts, the LaTeX summary for worksheets, and the قابلِ شیئر URL to resume the exact scenario in your next session.
Controls
Distribution (theory vs empirical)
Blue bars track empirical frequencies while the lighter overlay shows theoretical probabilities. Differences are labeled above each category for quick reference.
آزمائشوں کے ساتھ بدلتا تخمینہ
The solid line shows the running proportion. The dashed line marks the theoretical value and the shaded band gives the 95% confidence interval as trials accumulate.
Teaching tips
- Demonstrate the law of large numbers by increasing trials and letting learners watch the convergence band tighten around the theoretical line.
- Switch the dice to weighted mode and discuss how expected frequencies change and how the χ² statistic reacts to mis-specified weights.
- Highlight roulette's expected value and house edge to connect probability with finance-style expected returns.
عمومی سوالات
How کیا میں verify the RNG sequence in class?
Pick the published acceptance cases—e.g., seed 12345, 100 coin flips—then show how the simulator reports 44 heads every time. Switching devices yields the same outcome because the RNG and seed are fixed.
کیا میں export the run to شیئر کریں with students?
جی ہاں۔ خام گنتی اور چلتے تخمینے کے لیے CSV لیں، ورک شیٹس کے لیے LaTeX خلاصہ کاپی کریں، اور خودکار URL شیئر کریں تاکہ یہی تجربہ بعد میں دوبارہ کھل سکے۔