When the maths gets hard, simulate. Estimate pi with random points, get the birthday paradox right by brute force, and put honest error bars on any estimate.
3 units, about 3 hours. Free.
Estimate pi by simulation and explain how accuracy scales with the number of samples.
2Verify the birthday paradox by simulation and explain why intuition fails on combinations.
3Build bootstrap confidence intervals and explain what they honestly do and do not say.