Expected Value & Risk Assessment — Practice

Practice bank for UCAT Decision Making questions involving expected values, risk comparisons, and decision-making under uncertainty.

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Quick-Reference: Expected Value

Formula

$E(X) = \sum [\text{value of outcome} \times \text{probability of outcome}]$E(X)=∑[value of outcome×probability of outcome]

The expected value is the weighted average of all possible outcomes.

Example

A treatment has a 70% chance of full recovery (value = 10) and a 30% chance of partial recovery (value = 4).

$E = (0.70 \times 10) + (0.30 \times 4) = 7.0 + 1.2 = 8.2$E=(0.70×10)+(0.30×4)=7.0+1.2=8.2

Comparing Options

When comparing two options, calculate the expected value of each and compare. The option with the higher expected value is generally preferable (all else being equal).

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Quick-Reference: Risk Measures