Key Idea: A decision tree sets out the options, the chances of each outcome and what each is worth, so the options can be compared with one number each. This topic is drawing the tree, calculating it, and knowing when not to trust it.
Drawing it
- A square is a decision: the business chooses.
- A circle is a chance node: the outcome is uncertain.
- Each chance branch carries a probability; they add up to 1.
Calculating it
- Expected value = sum of probability × outcome.
- Net expected value = expected value − cost of the option.
- Choose the highest net figure; cross out the others.
Judging it
- The probabilities are estimates.
- It ignores risk: the worst case may be too big to bear.
- Qualitative factors can outweigh the numbers.
The words to know
| Word | Means | Do not confuse with |
|---|---|---|
| Decision node | a square: a point where the business chooses | a chance node, a circle |
| Chance node | a circle: a point where the outcome is uncertain | a decision node |
| Expected value | the average outcome, weighting each result by its probability | the most likely result |
| Net expected value | the expected value minus the cost of the option | the expected value before cost |
Multiply each outcome by its probability, add them, then take off the cost. Show every step and put the $ sign on the answer. Then say what the numbers leave out.
Exam-style question
Lena's Bakery Ltd could buy a delivery van for $30,000. There is a 0.6 chance it brings in $70,000 of extra contribution and a 0.4 chance it brings in $20,000. Calculate the net expected value of buying the van (show all your working).
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Important: The café corner's expected value, $60,000, beats the van's $50,000. Take off the costs and the van wins: $20,000 against $15,000.
Tap each card to check yourself.
What must the probabilities on one circle add up to? 1. Every possible outcome is on a branch.
Net expected value of the café corner? (0.7 × $90,000) + (0.3 × −$10,000) = $60,000; − $45,000 = $15,000.
Why might Lena still choose the café? If she thinks it will be busy more often than 0.7, or it builds the brand at Aisha's shop.
One advantage of a decision tree? It sets out every option and outcome clearly, so they can be compared with numbers.
One limitation? The probabilities and outcomes are estimates, so the answer is only as good as they are.
What does a cross on a branch mean? That option is rejected: it has the lower net expected value.
Exam tips
- Squares are decisions, circles are chances.
- Probabilities on one circle add up to 1.
- Expected value first, then take off the cost.
- Show every multiplication and the $ sign.
- A decision needs the numbers and what they leave out.