Lesson 4D.7.2

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

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 4D.7.2, Expected monetary values and utility: 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. What is the expected monetary value of a set of outcomes?

    • The sum of the payoffs regardless of probability.
    • The sum of probability times payoff over all outcomes.
    • The average of the payoffs with equal weight.
    • The largest payoff times its probability.

  2. What is utility used for in decision analysis?

    • Measuring the number of outcomes.
    • Reflecting a decision maker's attitude to risk, so that alternatives can be compared.
    • Calculating the EMV of chance nodes only.
    • Replacing probabilities with weights.

  3. How does a risk-averse decision maker typically behave?

    • They ignore the probabilities altogether.
    • They value a sure amount more than a gamble with the same or higher EMV.
    • They always prefer the gamble with the highest possible payoff.
    • They are indifferent to all outcomes.

  4. How does a risk-seeking decision maker behave?

    • They prefer a gamble to a sure amount with the same EMV.
    • They use only the smallest payoff.
    • They always prefer a sure amount to a gamble.
    • Their utility function is always zero.

  5. How is the expected utility of a gamble calculated?

    • Take the largest utility in the gamble.
    • Sum the probability times the utility of each outcome.
    • Take the utility of the expected payoff only.
    • Sum the utilities without probabilities.

  6. When is EMV the same as expected utility?

    • When the utility function is linear in money.
    • When the probabilities are equal.
    • When the utility function is zero at zero money.
    • When all payoffs are negative.

  7. On a utility scale, which outcomes are usually assigned 0 and 1?

    • The mean outcome has utility 1 and the worst is -1.
    • The worst outcome has utility 0 and the best has utility 1.
    • Every outcome has utility equal to its money value.
    • All utilities must be negative.

  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 EMV 100 and a sure option B pays 80. Which is chosen under EMV?

    • Neither, since the EMVs are negative.
    • Option B, since its payoff is certain.
    • Option A, since its EMV of 100 exceeds 80.
    • Both are equal.

  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. With those utilities, which option has the higher expected utility?

    • Both are equal.
    • Option B, since 0.6 is greater than 0.5.
    • Option A, since its EMV is higher.
    • Neither can be compared.

  13. If U(80) = 0.4 instead, which option has the higher expected utility?

    • Both are equal.
    • Option A, since 0.5 is greater than 0.4.
    • Neither can be compared.
    • Option B, since 0.4 is greater than 0.5.

  14. A gamble has a 0.2 chance of 500 and a 0.8 chance of 0. Which is preferred under EMV to a sure 90?

    • Neither, since EMV must be above 150.
    • The gamble, since its EMV of 100 exceeds 90.
    • The sure 90, since 80% chance of nothing outweighs the rest.
    • Both, since EMV only matters for chance events.

  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 the same decision maker with U(x) = sqrt(x), is a sure 30 preferred to the gamble with expected utility 5?

    • No, the gamble, since its EMV of 50 exceeds 30.
    • Neither, since utilities cannot be compared.
    • Yes, the sure 30, since sqrt(30) is about 5.48, which exceeds 5.
    • Both are equal, since 50 minus 30 is 20.

  19. Why might two decision makers with the same EMV choose differently?

    • EMV values are randomly generated for each person.
    • They always have different probability estimates by definition.
    • Their utility functions differ, so their attitudes to risk differ.
    • One of them must have miscalculated the EMV.

  20. What must be checked before expected utility is used to rank options?

    • That the decision tree has exactly three branches.
    • That the utility values are consistent with the decision maker's preferences over outcomes.
    • That every payoff is positive.
    • That all probabilities are equal.

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