PMGT5891 Chap.9 Decision Trees and Risk-Informed Decisions
Decision Trees and Risk-Informed Decisions
This chapter covers the Week 9 toolkit for choosing between options when outcomes are uncertain. You learn the standard notation, with squares for choices and circles for chance events, then solve trees by rolling back expected monetary value from right to left.
The chapter adds a break-even probability test so you can say how firm a recommendation is, reads individual paths for the chance of a loss, and shows one simple way to fold expected risk cost into a benefit-cost ratio. The Carter Racing case closes the chapter with a warning about deciding from incomplete data.
What this chapter covers
- 01
Decision nodes and chance nodes
- 02
Expected value of a chance node
- 03
Rolling back a tree from right to left
- 04
Break-even probability and sensitivity
- 05
Path probabilities and the chance of a loss
- 06
Benefit-cost ratio adjusted for risk
- 07
Carter Racing and missing data
- 08
Limits of decision trees
Worked example · free
Build in house or buy a package: a cost tree
- +1Expected cost of building: $120k + 0.4 x $100k = $120k + $40k = $160k.
- +1Expected cost of buying: $165k + 0.1 x $50k = $165k + $5k = $170k.
- +1Costs are being minimised, so the decision node takes the lower value: build, saving $10k in expectation.
- +1Break-even: 120 + 100p = 170, so 100p = 50 and p = 0.5. Above a 50% delay chance, buying is cheaper.
Key terms
- Decision node
- A decision node is a square on a decision tree marking a point where the choice is within the decision maker's control.
- Chance node
- A chance node is a circle marking outcomes outside the decision maker's control, each carrying a probability, with the probabilities on its branches totalling 1.0.
- Expected monetary value
- Expected monetary value is the probability-weighted sum of the money outcomes leaving a chance node.
- Roll-back
- Roll-back is the solving procedure that works from the right-hand end of a tree to the left, valuing each chance node at its EMV and each decision node at its best option.
- Break-even probability
- Break-even probability is the value of an uncertain probability at which two options have equal EMV, so the preferred option changes on either side of it.
Decision Trees and Risk-Informed Decisions FAQ
Which shape stands for a decision in a decision tree and which for a chance event?
Squares mark decisions, the points where you choose between options, and circles mark chance events whose outcomes you cannot control. Branches leaving a square are alternatives; branches leaving a circle are outcomes with probabilities. Time runs left to right, so draw the tree in the order events actually happen, then solve it in reverse.
Does the option with the highest EMV always win?
Not automatically. EMV is a long-run average, so an option with a higher EMV can still carry a real chance of losing money on this occasion. List each path with its probability, report the chance of a loss, and say whether a risk-averse owner might prefer the safer option. The tree informs the decision rather than making it.
How do you adjust a benefit-cost ratio for risk?
The unit names an adjusted benefit-cost ratio but gives no single formula. One clear illustration is to divide benefits by costs plus the expected cost of the remaining risks, where expected cost is the sum of probability times impact. An option with a strong plain ratio but heavy exposure can then fall behind a safer alternative.
What is the Carter Racing case about?
A small racing team must decide within an hour whether to enter a televised race after repeated engine failures, with its mechanics disagreeing about the cause. Most groups choose to race. The case is built on the data used in the Challenger launch decision and is used to discuss bias, pressure and judging risk from incomplete information.
What are the main weaknesses of decision trees?
Trees become unwieldy quickly, because every extra option or uncertain event multiplies the branches, so they suit fairly simple choices. The bigger weakness is the input: probabilities are often judgement rather than solid data, and the answer is only as good as those estimates. Sensitivity checks such as a break-even probability help expose that weakness.
Exam move
Practise until you can draw and solve a two-option tree by hand in under ten minutes, because the unit says a simple tree may appear in the exam. Start every tree by writing the probabilities on each circle and checking they total 1.0. Then work right to left: compute each circle's EMV on its own line, carry the best value back to the square, and state the recommendation in words.
Finish with one sensitivity line, either a break-even probability or the chance of a loss on the preferred option. For the Carter Racing discussion, prepare two or three sentences on what data were missing and how pressure shaped the vote. Finally, rehearse the adjusted benefit-cost idea with your own numbers so you can explain why a ranking can change once risk is priced in.
Working through Decision Trees and Risk-Informed Decisions in PMGT5891? Sia is AskSia’s AI Project Management tutor — ask any PMGT5891 Decision Trees and Risk-Informed Decisions question and get a clear, step-by-step explanation grounded in how PMGT5891 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
