Skip to main content
MathidiaMathematics Academy
Operations research
Lesson 54 of 75
Challenge

Decision analysis

Objective. Compare decisions under uncertainty.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Decision analysis compares choices under uncertainty by structuring a decision tree with decision nodes, chance nodes and payoffs, then computing the expected monetary value (EMV) of each option by weighting outcomes by their probabilities. The decision with the highest EMV is preferred under risk-neutral assumptions. For example, an investment paying £1000 with probability 0.4 and £200 otherwise has EMV = 0.4(1000) + 0.6(200) = £520. Sensitivity analysis then checks how the chosen decision changes if probabilities or payoffs shift, and utility functions can replace EMV when the decision-maker is risk-averse.

Worked example

In a decision analysis of two business options, option A pays £8000 with probability 0.3 and £1000 otherwise; option B pays £4000 with probability 0.6 and £2000 otherwise. Using expected monetary value, which option should be chosen?

£8000.00
Money illustration for £8000
  1. 1Compute EMV(A) = 0.3(8000) + 0.7(1000) = 2400 + 700 = 3100.
  2. 2Compute EMV(B) = 0.6(4000) + 0.4(2000) = 2400 + 800 = 3200.
  3. 3Compare the two expected monetary values, 3100 for A and 3200 for B.
  4. 4Since EMV(B) exceeds EMV(A), option B maximises expected monetary value.

Answer: Option B

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. A common mistake is comparing only the best-case payoffs of each option rather than computing expected monetary value across all outcomes weighted by probability, which ignores how likely each outcome actually is.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard