4D.7.2 Expected monetary values and utility Quiz: Pearson Edexcel Further Maths, Unit 46

The 20 questions

1. How is the expected monetary value of a set of outcomes calculated?

   • Product of all payoffs
   • Weighted sum of payoffs
   • Arithmetic mean of payoffs
   • Maximum possible payoff

2. What property of a decision maker does a utility function measure?

   • Financial capital
   • Attitude to risk
   • Probability calculation
   • Total profit

3. Which option does a risk-averse decision maker prefer over a gamble with equal EMV?

   • Higher variance gamble
   • Sure payoff
   • Fair gamble
   • Riskier option

4. Which option does a risk-seeking decision maker prefer over a sure payoff of equal EMV?

   • Gamble
   • Risk-free asset
   • Sure payoff
   • Lower expected payoff

5. How is expected utility calculated for a set of uncertain outcomes?

   • Product of all utilities
   • Weighted sum of utilities
   • Arithmetic mean of utilities
   • Maximum utility value

6. Under what type of utility function is EMV decision-making identical to expected utility?

   • Linear utility
   • Exponential utility
   • Concave utility
   • Convex utility

7. On a standard utility scale, which outcome is assigned a utility value of 0?

   • Median outcome
   • Worst outcome
   • Best outcome
   • Most likely outcome

8. A risky option gives a 0.5 chance of 300 and a 0.5 chance of -100. What is its EMV?

   • 100
   • 50
   • 0
   • 200

9. Option A has an EMV of £100 and Option B pays a sure £80. Which is chosen under EMV?

   • Neither option
   • Option B
   • Option A
   • Either option

10. With U(300) = 1 and U(-100) = 0, what is the expected utility of option A?

    • 0
    • 1
    • 0.5
    • 0.6

11. If U(80) = 0.6, what is the expected utility of the sure option B?

    • 0.5
    • 1
    • 0.8
    • 0.6

12. Option A has expected utility 0.5 and Option B has expected utility 0.6. Which option is preferred?

    • Neither option
    • Option B
    • Option A
    • Either option

13. Option A has expected utility 0.5 and Option B has expected utility 0.4. Which option is preferred?

    • Neither option
    • Option A
    • Either option
    • Option B

14. A gamble has an EMV of £100 and a sure option pays £90. Which is chosen under EMV?

    • Either option
    • The gamble
    • The sure option
    • Neither option

15. A gamble pays 40 with probability 0.25 and 0 with probability 0.75. What is its EMV?

    • 10
    • 25
    • 40
    • 0

16. A gamble pays 0 or 100 with probability one half each. What is its EMV?

    • 100
    • 50
    • 25
    • 0

17. A decision maker has utility U(x) = sqrt(x). A gamble gives 100 with probability 0.5 and 0 with probability 0.5. What sure amount has the same utility as this gamble?

    • 10
    • 25
    • 5
    • 50

18. For utility function U(x) = sqrt(x), what is the utility of a sure £36 payout?

    • 36
    • 625
    • 6
    • 18

19. Why might two people with the same EMV make different decisions?

    • Calculation errors
    • Different EMVs
    • Different risk attitudes
    • Incorrect probabilities

20. What must utility values reflect for expected utility theory to rank options correctly?

    • Standard deviations
    • Personal preferences
    • Monetary values
    • Expected payouts

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