Lesson 4D.7.1

4D.7.1 Decision trees Quiz: Pearson Edexcel Further Maths, Unit 46

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 4D.7.1, Decision trees: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 46: Decision analysis, written with Revision Ninja.

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The 20 questions

  1. In a decision tree, how are decision nodes drawn?

    • As triangles.
    • As circles.
    • As squares.
    • As diamonds.

  2. How are chance nodes drawn in a decision tree?

    • As triangles.
    • As straight lines.
    • As squares.
    • As circles.

  3. At a decision node, what does the decision maker do?

    • Waits for chance to choose a branch.
    • Chooses the most favourable outcome among the branches.
    • Takes the average of all the branches.
    • Chooses the branch with the lowest probability.

  4. At a chance node, what is calculated?

    • The number of decisions after it.
    • The expected monetary value (EMV) of the branches.
    • The cost of the decision.
    • The maximum of the branch payoffs only.

  5. What do the end nodes of a decision tree show?

    • The probability of each route.
    • The profit or pay-off for each outcome.
    • The highest utility for each decision.
    • The number of stages remaining.

  6. What must be true of the probabilities on the branches leaving a chance node?

    • They sum to 1.
    • They equal the pay-offs.
    • They are negative for losses.
    • They sum to 100.

  7. How is a decision tree solved?

    • By working from left to right, starting with the first decision.
    • By working from the right-hand end nodes back to the left, folding back the values.
    • By following only the top branch.
    • By choosing branches in a random order.

  8. A product launch has a 0.3 chance of a profit of 200 and a 0.7 chance of a loss of 50. What is the EMV of launching?

    • 25
    • 10
    • 35
    • 60

  9. In that launch decision, what should be done if not launching gives 0?

    • Do not launch, since the loss branch is 50.
    • Launch only if the success probability is below 0.3.
    • Launch, since the EMV of 25 is higher than 0.
    • Either option, since the EMVs are equal.

  10. In the same launch decision, what is the EMV if the success probability is 0.5 instead?

    • 150
    • 125
    • 25
    • 75

  11. For the launch decision with payoffs 200 and -50, what success probability gives an EMV of zero?

    • 0.5
    • 0.3
    • 0.2
    • 0.25

  12. A chance node has a 0.6 chance of a payoff of 60 and a 0.4 chance of 0. What is its EMV?

    • 36
    • 30
    • 60
    • 24

  13. A chance node has probabilities 0.2, 0.3 and 0.5 with payoffs 100, 40 and -20. What is its EMV?

    • 18
    • 22
    • 40
    • 30

  14. A chance node has a 0.25 chance of 80 and a 0.75 chance of 20. What is its EMV?

    • 50
    • 20
    • 40
    • 35

  15. An option has a 0.5 chance of a payoff of 100 and a 0.5 chance of -40. What is its EMV?

    • 60
    • 30
    • 40
    • 20

  16. A decision node compares a chance node with EMV 35 against a sure payoff of 40. Which is chosen?

    • Both are equal.
    • Neither, since 35 and 40 cannot be compared.
    • The sure payoff of 40.
    • The chance node with EMV 35.

  17. A chance node has EMV 22 and the sure option is 20. Which option is chosen when folding back?

    • The one with the largest single payoff only.
    • The sure option, since it has no risk.
    • Neither, since decision nodes cannot compare EMVs.
    • The chance node, since its EMV of 22 is above 20.

  18. Investing costs 10 at the start and then yields an EMV of 25 from a chance node. What is the net EMV of investing?

    • 35
    • 15
    • 10
    • 25

  19. Why might a decision maker prefer an option with a lower EMV?

    • EMVs must be whole numbers to be compared.
    • EMV is always the same as profit, so there is no reason.
    • Chance nodes cannot be used in decisions.
    • Their utility function can make a sure amount preferable to a riskier gamble with a higher EMV.

  20. What does a sensitivity analysis on the probabilities in a decision tree check?

    • Whether all payoffs are positive.
    • Whether the tree has the correct number of nodes.
    • Whether the decision maker prefers risk.
    • How much the best decision changes when the probabilities are varied.

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