cs-121 — The Umbrella Decision
| Field | Value |
|---|---|
| id | cs-121 |
| difficulty | Beginner |
| topics | expected value, payoffs |
| lecture | lecture-31 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | none |
| objective | state inputs, outputs, and assumptions, then solve a small instance by hand |
| solution | held by the instructor; discussed after the attempt |
Problem
Carry an umbrella or not under a 30% rain chance with asymmetric costs. Payoff table, expected values, and why the bigger loss dominates.
Your deliverable is the stated assumptions, the expected value computed for the worked instance, the hidden assumption named, and one contested case. 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: rain 30%; umbrella: carry cost 2 (bother); caught in rain cost 10
- Output: EV carry = -2 always; EV leave = 0.7x0 + 0.3x(-10) = -3 -> carry wins despite 70% sunny
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
- Payoff table first, then EVs. The asymmetric loss makes 30% rain 'usually carry' weather.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Propose one extra rule that would change the verdict — is it an improvement?"
Constraints and assumptions
- Difficulty: Beginner (no prior experience assumed).
- Topics: expected value, payoffs.
- 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: Compute the flip point where the decision changes and defend the threshold.