cs-113 — Dice Before Data

Problem

Simulate 10,000 rolls of two dice; compare the sum distribution to theory. Building the generator and trusting the sample.

Your deliverable is the simulation result with trials and spread, the one-trial story, and the comparison with exact reasoning. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.

Examples

• Input: two dice, 10,000 rolls
• Output: sum 7 ~ 16.7% (6/36 exact); distribution matches theory within ~1%

Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.

What to notice

• One trial = roll two dice. The only skill is the loop and the comparison table.
• A simulation is only as good as the story of one trial.
• Error shrinks like 1/sqrt(trials) — quadruple the work, halve the error.

Discussion starter

After the solution is revealed, the class spends five minutes on this prompt: "How many trials would you demand before believing a 1-in-1000 event estimate?"

Constraints and assumptions

• Difficulty: Beginner (no prior experience assumed).
• Topics: simulation, randomness.
• Classroom-scale inputs unless the problem says otherwise.
• Time-box: about five minutes for a first attempt; partial answers with clear reasoning are worth more than silent struggling.
• Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.

Hints and extension

• First nudge: identify the pattern the worked instance uses before computing anything.
• If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
• After the reveal, attempt the extension below before the next lecture.
• Extension challenge: Halve and double the trial count; report how the estimate wobbles.