Probability Cards
Simulation lab: experiment vs theory
Ages 14+ · about 35 minutes
Name:
Class:
Date:
Goal: See how experimental frequency approaches theoretical probability and how error shrinks as samples grow.
Remember: Exact probability of one pair is 1,098,240 ÷ 2,598,960 = 42.26%. Error = |observed − exact| in percentage points.
Lab steps
- Open the five-card pattern simulator on the website (Simulators, then Five-card pattern frequencies).
- Type the seed classroom into the seed box.
- Choose 100 samples and press Run simulation. Write the count for One pair in the table below.
- Repeat for 1,000, 10,000 and 100,000 samples with the same seed.
- Complete the table: observed % = count ÷ samples × 100; error = |observed % − 42.26|.
| Samples | One pair count | Observed % | Exact % | Error (points) |
|---|---|---|---|---|
| 100 | 42.26 | |||
| 1,000 | 42.26 | |||
| 10,000 | 42.26 | |||
| 100,000 | 42.26 |
1.Complete the results table (it is printed above these questions).
2.Which sample size gave the smallest error? Is that what you expected?
3.The predicted standard error is √(p(1 − p) ÷ n) with p = 0.4226. Calculate it (in percentage points) for n = 100 and n = 10,000.
4.Change the seed to mylab and run 100 samples again. Is the count the same as before? Why or why not?
5.By what factor must the number of samples increase to halve the typical error?