Back to Planning and Decision Making

Higher Applications of Mathematics

Expected value

Comparing outcomes using probability and value.

Planning referencePlanning mixed quiz

Planning reference

Check networks, timing, float, PERT, Gantt charts, risk and expected value.

Mixed revision quiz

Review Planning and Decision Making with adaptive feedback.

Before you start

  • Be confident reading information from tables and diagrams.
  • Check time units, costs and probabilities before calculating.
  • Be ready to explain what the result means for the project or decision.

Method helper

Which planning method do I use?

Do tasks depend on other tasks being completed first?

Draw an activity network.

Are task times uncertain?

Use PERT estimates.

Do you need the minimum project duration?

Find the critical path.

Do you need to know which activities can be delayed?

Calculate float.

Do you need to show a project schedule on a timeline?

Create a Gantt chart.

Are you comparing uncertain financial outcomes?

Calculate expected value.

Are you comparing options with risk, cost and benefit?

Use risk and decision making.

Do you need a written recommendation?

Explain the decision in context with limitations.

Planning lesson

Key idea

  • This topic focuses on comparing uncertain options using probabilities, values and long-run averages. Planning and decision making uses mathematics to organise real projects and compare choices under constraints.
  • A good planning answer identifies the activities or options, uses the correct method, and explains the result in the context of the project.
  • For Higher Applications, the conclusion matters. You should mention timing, risk, cost, uncertainty or limitations where they affect the decision.

Key definitions, methods and formulae

  • Expected value = sum of probability x outcome.
  • Probabilities should add to 1 for a complete set of outcomes.
  • Expected value is a long-run average, not a guaranteed result.

Worked examples

Planning walkthrough 1

Set up the information

A small Scottish business compares delivery insurance options for parcels during winter.

  1. List each possible outcome and its probability.
  2. Multiply each value by its probability.
  3. Add the products to find the expected value.

Expected value gives a numerical basis for comparing uncertain options.

Planning walkthrough 2

Carry out the method

A small Scottish business compares delivery insurance options for parcels during winter.

  1. Compare expected values for two options.
  2. Include costs such as premiums or fees.
  3. Choose the option with the better expected outcome if other factors are similar.

Costs must be included for a fair comparison.

Planning walkthrough 3

Interpret the decision

A small Scottish business compares delivery insurance options for parcels during winter.

  1. Explain the limitation of expected value.
  2. Consider risk tolerance and worst-case outcomes.
  3. Write a decision sentence that includes context.

A decision may consider risk as well as the expected value.

Watch out

  • Ignoring dependencies and allowing activities to start too early.
  • Mixing time units, such as hours and days, without converting.
  • Choosing the cheapest option without considering risk or impact.
  • Treating expected value as a guaranteed outcome.
  • Giving a schedule or calculation without explaining what it means for the project.

Connected topics

Related Higher Applications topics

Finance: InsuranceStatistics: Probability, tree diagrams and Venn diagrams

Next step

Move into practice

Use the learning notes to read dependencies and constraints, then try varied schedules, precedence tables and decision contexts.

Planning mixed quiz