Further Mathematics · Pearson Edexcel 9FM0 · Option D2 · Topic 7

Decision analysis

Decision trees, expected monetary value and utility.

  • 2 sub-topics
  • Taught in Year 13
  • 29 practice questions
  • 2 animated lessons
Practice questions (29) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 7.1Decision treesY13
  2. 7.2Expected monetary value and utilityY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 29 questions in this topic, free, no account needed.

Decision analysis

Not needed for Year 12Easy

Nodes in a decision tree · Year 13 · 1 mark

  1. In a decision tree, what does a circle stand for?
    (1)

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  1. The tree is evaluated from right to left: expected values at chance nodes, the best option at decision nodes.BB: A chance node: the branches happen with given probabilities

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Decision analysis

Not needed for Year 12Medium

Decision trees · Year 13 · 5 marks

A company can sell an idea now for £30000, or develop it at a cost of £30000. If developed, the product succeeds with probability 0.4, earning £120000, or fails, earning £10000.
  1. (a)
    Draw a decision tree to represent this situation.
    (2)
  2. (b)
    Use expected monetary value to decide what the company should do.
    (3)
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Part (a)2 marks

  1. Show pay-offs at the ends.A decision node with two branches; the 'develop' branch leads to a chance node with probabilities 0.4 and 0.6.

Part (b)3 marks

  1. EMV(develop)\text{EMV(develop)}=0.4(120000){}= 0.4(120000)+0.6(10000){}+ 0.6(10000)−30000{}- 30000
  2. =24000= 24000
  3. Since 24000<3000024000 < 30000, sell the idea.

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Decision analysis

Not needed for Year 12Hard

Expected monetary value and utility · Year 13 · 6 marks

Jo can accept £144 now, or play a game that pays £400 with probability 0.4 and nothing otherwise. Jo's utility for £x is x\sqrt{x}.
  1. (a)
    Find the expected monetary value of the game, and say which option maximises EMV.
    (2)
  2. (b)
    Use expected utility to decide what Jo should do.
    (3)
  3. (c)
    Explain why the two methods can give different decisions.
    (1)
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Part (a)2 marks

  1. 0.4×400=1600.4 \times 400 = 160
  2. The game maximises EMV.

Part (b)3 marks

  1. EU(game)\text{EU(game)}=0.4400{}= 0.4\sqrt{400}=8{}= 8
  2. Compare and decide: take the money.U(sure)=144=12\text{U(sure)} = \sqrt{144} = 12

Part (c)1 mark

  1. A concave utility function models risk aversion: certain money is valued more than a risky gamble with the same EMV.

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