Risk Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Risk.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept 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?

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Risk combines probability and impact—low probability + high impact can be serious.

Common stuck point: People often misjudge risk—overweighting dramatic risks, underweighting common ones.

Sense of Study hint: Make a quick two-column list: probability of the bad outcome and its cost. Multiply them to get the expected loss for comparison.

Worked Examples

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.

Solution

  1. 1
    Expected loss A: E_A = P(A) \times \text{cost} = 0.10 \times 50000 = \5,000$
  2. 2
    Expected loss B: E_B = P(B) \times \text{cost} = 0.02 \times 500000 = \10,000$
  3. 3
    Compare: E_B = \10,000 > E_A = \5,000 — data breach poses greater expected financial risk
  4. 4
    Interpretation: despite being less probable, the data breach's high cost makes it the bigger financial threat

Answer

Expected loss: Equipment = \5,000; Data breach = \10,000. Data breach is the greater financial risk.
Expected loss = Probability × Magnitude. A rare but catastrophic event can have greater expected loss than a common but minor one. Risk management must consider both frequency and severity of potential losses.

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.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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 2

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?
← Back to Risk Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

probability