F18 · Topic 3.15
Exact chance versus a trial stream
1. Predict first
For integers 1…10 and success≤3, predict the exact probability and expected successes in 20 independent trials.
Change it · step through · explain
Change an input, predict what will happen, then advance one step. Read why the state changes, reset and experiment. This fixed teaching model does not save progress or award XP.
Ready · Make a prediction
- Input 13Waiting
Ready to experiment
Why: Predict the first change, then advance one step.
Try this: Try thresholds 0 and 10. The supplied stream is deterministic, not randomly regenerated.
2. Build your procedure
Write a 20-trial simulator that counts successes for RANDOM(1,10)≤3 and displays successes/20. Specify initialization and loop placement.
Use AP CSP pseudocode, a language you know, or precise plain language. Your code is not executed here. Use the classroom assignment to save your response.
3. Check boundaries
| Input | Expected | Why this case |
|---|---|---|
| Range 1…10, threshold 3 | 3 successful values of 10; probability 0.3 | Inclusive range. |
| Range 1…10, threshold 0 | 0 of10 | Impossible event. |
| Range 1…10, threshold 10 | 10 of10 | Certain event. |
4. Explain and reflect
The fixed stream has four successes in ten entries. Does this invalidate the theoretical 3/10 probability?
Model limits: The supplied stream is deterministic for reproducibility. It demonstrates counting, not independent random sampling or secure randomness.