Decision trees and expected monetary valueEdexcel A-Level Further Maths: Mind map

Exam questions on Decision trees and expected monetary value

1. A florist must decide whether to order a large or a small stock of roses for a weekend. The weather will be fine with probability 0.6 or poor with probability 0.4. A large stock gives a profit of £800 if the weather is fine and £200 if it is poor. A small stock gives a profit of £500 if fine and £350 if poor.
   The probability of fine weather is $p$ instead of $0.6$. Find the value of $p$ for which the two stock sizes have the same EMV.2 marks
2. A company must choose between two projects. Project X gives a certain profit of £40 000. Project Y gives a profit of £100 000 with probability 0.5, and otherwise a loss of £20 000.
   The directors assign a utility of 0 to a loss of £20 000, 0.8 to a profit of £40 000 and 1 to a profit of £100 000. Calculate the expected utility of each project and state which the company should choose.2 marks
3. A software firm is deciding whether to launch a new app. Without any research, the probability that the app succeeds is 0.5. A success gives a profit of £120 000 and a failure gives a loss of £50 000; not launching gives £0. Alternatively, the firm can first pay £10 000 for a market survey. The survey result is favourable with probability 0.6, and then the probability of success is 0.75; otherwise it is unfavourable, and then the probability of success is 0.125. The profits and losses above do not include the cost of the survey.
   Find the EMV of launching the app after an unfavourable survey result, and state the decision the firm should then make.3 marks