Room for one new project: With the Station Road shop open from September, Priti says her bakers can take on one more project next summer. Only one.
Lena's idea
- A stand at the town's summer food festival
- Depends on the weather
Marco's idea
- A weekend catering service for weddings and parties
- Depends on how many couples book
Neither is a sure thing.
They could argue about it over coffee. Instead, Marco draws the choice on one sheet of paper, from left to right: the two options, what could happen after each one, how likely each result is, and the money each result would bring in.
That drawing is a decision tree: a diagram that maps a decision, its possible outcomes, their probabilities and their money values, so that managers can compare options on numbers rather than on a hunch.
| The question | Where the tree answers it | On Lena and Marco's tree |
|---|---|---|
| What can we do? | The options, drawn as branches from a square | Festival stand, or weekend catering |
| What might happen? | The outcomes, drawn as branches from a circle | A dry or a wet festival weekend; many or few bookings |
| How likely is each? | A probability written on each outcome | A dry weekend 0.6, a wet one 0.4 |
| What would we earn? | The money at the end of each branch | $5,000 of sales if dry, $1,500 if wet |
Read it like a timeline: A decision tree runs left to right, in the order things happen. First the business chooses. Then something it cannot control happens. Then the money comes in.
Every path from left to right is one possible future for the business.
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A decision tree is drawn with two shapes, and each one means something different. Get them right and anyone can read the tree; swap them and it says the business controls the weather.
Marco's tree, from left to right
A square: the decision
The square (a decision node) is where Lena and Marco choose. It is theirs to decide, so it sits at the left, before anything else happens.
Branches from the square: the options
One line for each option, labelled with what it is and what it costs: 'Festival stand, $800' and 'Weekend catering, $1,500'.
A circle: chance takes over
At the end of each option sits a circle (a chance node). From here the result is out of their hands: the weather, or the number of bookings, decides it.
Branches from the circle: the outcomes
One line for each thing that could happen, each with its probability: 'Dry weekend, 0.6' and 'Wet weekend, 0.4'.
The end of each branch: the money
The figure the business would receive if that path came true (the outcome, or payoff): $5,000 of sales on a dry weekend, $1,500 on a wet one.
A general example, not Lena's bakery: a business choosing between expanding its factory and marketing online. The square is the decision, each circle is a chance node, every outcome carries a probability and a money value, and the cross marks the option not taken. The key under the tree says which shape is which.
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Square or circle?: Ask one question at each point: who decides what happens next?
If the business decides, it is a square. If the weather, the customers or the economy decides, it is a circle. The festival stand is a square branch; a wet weekend comes from a circle.
A tree needs a key, a small note beside it saying that a square is a decision and a circle is a chance event. Without one, a reader cannot tell a choice from a gamble.
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How likely is a dry festival weekend? Marco checks the town's records: six of the last ten festivals were dry. So he writes 0.6 on the dry branch.
That number is a probability: how likely an outcome is, on a scale from 0 (it will never happen) to 1 (it is certain). 0.6 is the same as 60%, or 6 times in 10.
At every circle, the probabilities add up to 1: The branches leaving a circle cover everything that can happen there, so their probabilities always total 1. Dry 0.6 plus wet 0.4 makes 1.
If they come to 0.9 or 1.1, an outcome is missing or a number is wrong. Probabilities come from past records, market research, or a manager's best estimate.
The expected value of the festival stand
Take each outcome
Dry weekend: $5,000 of sales, probability 0.6. Wet weekend: $1,500 of sales, probability 0.4.
Multiply each by its probability
0.6 × $5,000 = $3,000. 0.4 × $1,500 = $600.
Add the results
$3,000 + $600 = $3,600. That is the expected value at the festival circle.
Expected value = (probability × outcome) + (probability × outcome), one bracket for each branch leaving the circle.
The expected value (also called expected monetary value, or EMV) is the average result the option would give if the same choice could be made again and again. Each outcome counts in proportion to how likely it is, so the dry weekend pulls the figure towards $5,000.
An average, not a forecast: The festival will never bring in exactly $3,600. It brings in $5,000 or $1,500, depending on the weather.
The expected value is what the stand earns on average over many summers. It is a way of weighing the good and the bad outcomes together, not a prediction of next July.
What the sheet of paper changed: Before the tree, Lena and Marco each had a favourite and a feeling. After it, both options sit side by side on one page, each with its cost, its outcomes, their probabilities and their money.
That is what a decision tree gives a business: the same decision, laid out so that it can be reasoned about.
Clear and visual
- The whole problem on one page, in the order it happens
- Lena, Marco and Priti can all read it and argue about the same numbers
Every option at once
- The festival and the catering are set out together, not one at a time
- Seeing them together speeds up the decision
Risk in the open
- Each outcome carries its probability: a 0.4 chance of a wet weekend is written down, not forgotten
- Managers must think about what could go wrong, not only what could go right
Numbers, not hunches
- Costs and returns of each option are written on the branches
- Expected values give a logical, numerical basis for the choice
An advantage of the tree, not of the option: 'The catering could earn $10,000' is a reason to like the catering. It says nothing about the decision tree.
An advantage of using a decision tree is about the tool: what drawing the tree lets the business see or do that it could not before.
To explain one advantage, name it, then show it in the case: which options the tree sets side by side, which risk it puts a number on, which costs and returns it lets the owner compare. The case's own names and figures turn a general point into an explanation.
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How this comes up: A case gives a business with two or three options and a table of costs, probabilities and expected returns.
After the tree has been drawn, a short question follows: explain one advantage for the owner of using a decision tree, for two marks.
Two moves: One advantage of the tool, then what it does for this owner, with this owner's options.
The two-mark pattern
- Name the advantage. The tree sets out the options, their outcomes and probabilities on one page, so the decision is clear and logical.
- Develop it for the owner. Lena and Marco can see the festival and the catering side by side, each with its cost, its risk and its possible sales, and compare them on numbers.
Three ways to lose the second mark: No case. 'It is visual and easy to understand' fits any business. Name the options and a figure.
The option, not the tool. Why the catering is a good idea is not an advantage of a decision tree.
A limitation. The question asks for an advantage; a point about probabilities being guesses answers a different question.
Explain one advantage for Lena and Marco of using a decision tree.
Model answer plan
See the answer broken into clear points, with guidance on how each point earns marks.