Decision Under Uncertainty Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

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

Solution

  1. 1
    Expected value of bringing umbrella: E(bring)=−1E(\text{bring}) = -1 (certain cost)
  2. 2
    Expected value of not bringing: E(no umbrella)=0.4(−10)+0.6(0)=−4E(\text{no umbrella}) = 0.4(-10) + 0.6(0) = -4
  3. 3
    Optimal decision: bring umbrella (−1>−4-1 > -4)
  4. 4
    Interpretation: expected cost is 4 times worse without umbrella — bring it

Answer

Bring umbrella (EV=-1) vs. don't bring (EV=-4). Bringing umbrella is optimal under expected value.
Decision under uncertainty uses expected value to compare options with probabilistic outcomes. Each option is evaluated by its probability-weighted average outcome. The action with the highest (or least negative) expected value is optimal for a risk-neutral decision-maker.

About Decision Under Uncertainty

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

Learn more about Decision Under Uncertainty →

More Decision Under Uncertainty Examples

Example 2 hard

A startup has three investment options: A (safe: gain [formula]80K, 30% chance [formula]200K, 70% ch

Example 3 easy

You can either (A) study for certain +10 points on the final, or (B) not study: 50% chance +20 point

Example 4 hard

A city decides whether to build a flood barrier (cost [formula]50M; damage with barrier: $5M. Calcul

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