Decision Analysis

Edexcel

A2 June 2025 Q1

EdexcelCurrent spec3 marksDecision Analysis

1. Ravi can choose one of three options, A, B or C, when playing a game. The profit, in pounds, associated with each outcome, and the corresponding probabilities, are shown in the decision tree in Figure 1.

Figure 1: decision tree. Decision node with branches A, B and C. A leads to a chance node with outcomes 0.55: 370, 0.25: 250, 0.2: -75. B leads to a chance node with outcomes 0.75: 245, 0.25: 195. C leads to a chance node with outcomes 0.45: 390, 0.4: 325, 0.15: -280
Figure 1

Calculate the optimal EMV to determine Ravi’s best course of action. You must make your working clear. (3)

A2 June 2024 Q5

EdexcelCurrent spec10 marksDecision Analysis

5. Sebastien needs to make a journey. He can choose between travelling by plane, by train or by coach.

Sebastien knows the exact costs of all three travel options, but he also wants to account for his travel time, including any possible delays.

The cost of Sebastien’s time is £50 per hour.

The table below shows the costs, the journey times (without delays), and the corresponding probabilities of delays, for each travel option.

Cost of travel optionJourney time (in hours) without delaysProbability of a 1-hour delayProbability of a 2-hour delayProbability of a 3-hour delayProbability of a 24-hour delay
Plane£20030.090.0500.03
Train£13050.070.0300
Coach£7060.150.10.050
(a) By drawing a decision tree, evaluate the EMV of the total cost of Sebastien’s journey for each node of your tree. (6)
(b) Hence state the travel option that minimises the EMV of the total cost of Sebastien’s journey. (1)
(c) A cube root utility function is applied to the total costs of each option. Determine the travel option with the best expected utility and state the corresponding value. (3)

A2 June 2023 Q2

EdexcelCurrent spec5 marksDecision Analysis

2. An outdoor theatre is holding a summer gala performance. The theatre owner must decide whether to take out insurance against rain for this performance.

The theatre owner estimates that

  • on a fine day, the total profit will be £15 000
  • on a wet day, the total loss will be £20 000

Insurance against rain costs £2 000. If the performance must be cancelled due to rain, then the theatre owner will receive £16 000 from the insurer. If the performance is not cancelled due to rain, then the theatre owner will receive nothing from the insurer.

The probability of rain on the day of the gala performance is 0.2

Draw a decision tree and hence determine whether the theatre owner should take out the insurance against rain for this performance. (5)

A2 June 2022 Q3

EdexcelCurrent spec7 marksDecision Analysis

3. The table below shows the transport options, usual travel times, possible delay times and corresponding probabilities of delay for a journey. All times are in minutes.

Transport optionUsual travel timePossible delay timeProbability of delay
Car52100.10
250.02
Train45150.05
250.03
Coach5550.05
150.01
(a) Draw a decision tree to model the transport options and the possible outcomes. (5)
(b) State the minimum expected travel time and the corresponding transport option indicated by the decision tree. (2)

A2 October 2021 Q2

EdexcelCurrent spec7 marksDecision Analysis

2. Alka is considering paying £5 to play a game. The game involves rolling two fair six-sided dice. If the sum of the numbers on the two dice is at least 8, she receives £10, otherwise she loses and receives nothing.

If Alka loses, she can pay a further £5 to roll the dice again. If both dice show the same number then she receives £35, otherwise she loses and receives nothing.

(i) Draw a decision tree to model Alka’s possible decisions and the possible outcomes.
(ii) Determine Alka’s optimal EMV and state the optimal strategy indicated by the decision tree. (7)

A2 October 2020 Q2

EdexcelCurrent spec7 marksDecision Analysis

2. Jenny can choose one of three options, A, B or C, when playing a game. The profit, in pounds, associated with each outcome and their corresponding probabilities are shown on the decision tree in Figure 1.

Decision tree: a decision node with branches A, B and C, each to a chance node. A: probability 0.6 to 350 and 0.4 to −140. B: probability 0.75 to 260 and 0.25 to −190. C: probability 0.8 to 220 and 0.2 to −230
Figure 1
(a) Calculate the optimal EMV to determine Jenny’s best course of action. You must make your working clear. (3)

For a profit of £\(x\), Jenny’s utility is given by \(1 - \mathrm{e}^{-\frac{x}{400}}\)

(b) Using expected utility as the criterion for the best course of action, determine what Jenny should do now to maximise her profit. You must make your working clear. (4)

A2 June 2019 Q7

EdexcelCurrent spec12 marksDecision Analysis

7. Aisha is deciding whether or not to play a game.

The game involves rolling three fair six-sided dice, which have faces numbered from 1 to 6

If the total score on the three dice is 16 or more then she wins a prize. If the total score is 15 or less then she loses and will have to pay the person running the game £3

(a) Given that the prize is £15
(i) draw a decision tree to model Aisha’s possible decisions and the possible outcomes
(ii) determine Aisha’s optimal EMV and state the optimal strategy indicated by the decision tree. (6)

The utility function of the game to Aisha is \(\mathrm{u}(m) = 1 - \mathrm{e}^{-\frac{m}{500}}\) where \(m\) is the amount of money that Aisha has available. Given that Aisha has exactly £3 and that the prize is now £\(x\)

(b) find the expected utility to Aisha of playing the game in the form\[\frac{a}{b}\left(1 - \mathrm{e}^{-\frac{(x+c)}{500}}\right)\]where \(a\), \(b\) and \(c\) are integers to be found. (2)

Aisha decides to use the expected utilities to determine whether she should play the game or not.

(c) Find the minimum prize for which Aisha would consider playing the game. (4)