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

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. In a decision tree, what shape represents a decision node?

   • Double circle
   • Square
   • Triangle
   • Circle

4. What value is calculated at a chance node in a decision tree?

   • Certainty equivalent
   • Expected monetary value
   • Utility index
   • Maximum payoff

5. What is displayed at the end nodes of a decision tree?

   • Expected monetary value
   • Payoff
   • Decision choice
   • Probability

6. What must the probabilities on branches leaving a chance node sum to?

   • 1
   • 100
   • 0.5
   • 0

7. What is the process of evaluating a decision tree from right to left called?

   • Forward tracking
   • Folding back
   • Pruning branches
   • Sensitivity analysis

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. A decision node offers a branch with EMV 25 and another with payoff 0. Which is chosen?

   • Payoff of 0
   • Both branches
   • EMV of 25
   • Neither branch

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 EMV 35 against a sure payoff of 40. Which option is chosen?

    • Average of 37.5
    • Neither option
    • Sure payoff of 40
    • EMV of 35

17. A decision node offers a chance node with EMV 22 or a sure option of 20. Which is chosen?

    • Both options
    • Sure option
    • Neither option
    • Chance node

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 select an option with a lower expected monetary value?

    • Linear utility
    • Risk neutrality
    • Risk seeking
    • Risk aversion

20. What does sensitivity analysis on branch probabilities in a decision tree test?

    • Expected monetary value
    • Calculation accuracy
    • Total probability sum
    • Stability of decision

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