Practice Decision Under Uncertainty in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Decision under uncertainty involves choosing between options whose outcomes are not known for certain, typically by comparing expected values or risk profiles.

The rational strategy under uncertainty is not always to pick the option with the best single outcome but the one with the best expected outcome weighted by its probability.

Example 1

medium
An umbrella decision: if you bring an umbrella, you carry it all day (cost: mild inconvenience, -1). If you don't bring it and it rains (prob 0.4), you get wet (cost: -10). If you don't bring it and it doesn't rain (prob 0.6), cost is 0. Calculate expected values for both decisions.

Example 2

hard
A startup has three investment options: A (safe: gain \50K certain), B (medium: 70% chance \80K, 30% chance \0), C (risky: 30% chance \200K, 70% chance -\20K$). Calculate EV for each and identify which a risk-neutral investor and a risk-averse investor would choose.

Example 3

easy
You can either (A) study for certain +10 points on the final, or (B) not study: 50% chance +20 points, 50% chance +0 points. Calculate EV for both and decide.

Example 4

hard
A city decides whether to build a flood barrier (cost \10M). Flood probability in 50 years: 0.30; flood damage if no barrier: \50M; damage with barrier: \$5M. Calculate expected costs for building vs. not building.
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