Decision analysis

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.

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

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.

Draw a decision tree to model the transport options and the possible outcomes.

State the minimum expected travel time and the corresponding transport option indicated by the decision tree.

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.

Draw a decision tree to model Alka’s possible decisions and the possible outcomes.

Determine Alka’s optimal EMV and state the optimal strategy indicated by the decision tree.

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.

Calculate the optimal EMV to determine Jenny’s best course of action. You must make your working clear.

For a profit of £x, Jenny’s utility is given by 1 e

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.

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

Given that the prize is £15

draw a decision tree to model Aisha’s possible decisions and the possible outcomes

determine Aisha’s optimal EMV and state the optimal strategy indicated by the decision tree.

The utility function of the game to Aisha is u(m) = 1 – e where m is the amount of money that Aisha has available. Given that Aisha has exactly £3 and that the prize is now £ x

find the expected utility to Aisha of playing the game in the form

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

Find the minimum prize for which Aisha would consider playing the game.