Practice Risk in Math

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

Quick Recap

The possibility of loss or negative outcome, often quantified by probability and severity.

What could go wrong, how likely is it, and how bad would it be?

Example 1

medium
A business faces two possible disasters: (A) equipment failure — probability 0.10, cost \50,000; (B) data breach — probability 0.02, cost \500,000. Calculate the expected loss from each and determine which poses greater financial risk.

Example 2

hard
Should you buy insurance for \200/year that covers a \5000 loss occurring with probability 0.03? Calculate expected value for both choices and discuss why someone might still buy the insurance.

Example 3

easy
A lottery ticket costs \2 and pays \1,000,000 with probability \frac{1}{2,000,000}. Calculate the expected value and determine whether this is a good financial decision.

Example 4

hard
Two investment options: A = certain gain of \500; B = 60% chance of \1000, 40% chance of \$0. Calculate EV for both. Which would a risk-neutral person choose? A risk-averse person?
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