What it means
The diagram starts at a single point on the left, called the root. From there, lines branch out for each possible choice or event, and each of those can branch again, until every path ends in a final outcome.
There are two main uses. A probability tree shows chance events and the likelihood of each, and a decision tree adds choices that a manager can make, such as whether to launch a product, build a plant or accept a contract.
To use the tree, you multiply the probabilities along each path to find the chance of that outcome. You then multiply each outcome by its payoff and add the results, which gives the expected monetary value (the probability-weighted average result).
Decision trees are worked from right to left. You first calculate the value at the ends of the branches, then step back to each decision point and choose the option with the best expected value.
The method forces clear thinking. It makes assumptions visible, shows which uncertainties matter most, and helps teams to discuss numbers rather than opinions.
A tree can be drawn on a whiteboard in minutes and refined as new information arrives. Its limits are worth remembering.
The answer is only as good as the probabilities and payoffs, which are often estimates, and the expected value ignores how much risk a business can bear if the worst outcome happens.
In practice
Real-world examples.
Example
A drinks company is considering a test market before a national launch. The tree shows the cost of the test, the chance it gives a positive signal, and the payoff of each decision afterwards. The team can see at a glance whether paying for the test is worth the information it provides.
Example
A lender estimates the chance that a borrower will repay in full, repay late or default. The tree helps to work out the expected loss on a $100,000 loan and the interest rate needed to cover it. The lender updates the probabilities each year as it collects its own repayment history.
Example
A biotech start-up maps the stages of drug development, with a probability of success at each stage. The tree shows the chance of reaching the market and the value of the project at the start. Investors use the result to decide how much to pay for a share of the company.
Formula
Calculation
The expected monetary value of a choice is:
Expected monetary value = Sum of (Probability of outcome x Payoff of outcome)
An illustrative company is deciding whether to launch a new product. There is a 60% chance of success, with a profit of $500,000, and a 40% chance of failure, with a loss of $200,000. The expected value is (0.60 x $500,000) + (0.40 x -$200,000) = $300,000 - $80,000 = $220,000. If the alternative is to do nothing, which has a value of $0, the launch has the higher expected value, though the company must be able to survive the $200,000 loss.Case study
Seen in the real world.
Kingsley Outdoor Gear is an illustrative, fictional manufacturer that had to choose between building a new factory for $4,000,000 and renting extra capacity for $900,000 a year. Demand for its new tent range was uncertain, so the finance team built a tree.
They estimated three demand outcomes: high at 30%, medium at 50% and low at 20%. For each outcome they estimated the profit from building and from renting, including the cost of unused capacity.
The tree showed that building had a slightly higher expected value, but a loss of $1,500,000 in the low demand case. In this illustrative decision, the board chose the rental option, accepting a smaller expected return to avoid a loss it did not want to risk. The finance team kept the tree on file and updated it each quarter as actual sales came in.
Watch out
Common mistakes.
- Treating estimated probabilities as facts, when they are judgements that should be tested. Try changing each probability by 10 percentage points to see whether the decision changes.
- Forgetting that branches from one point must have probabilities that add up to 100%.
- Choosing by expected value alone, without checking whether the business can survive the worst outcome. A positive average is no comfort if the bad case ends the business.
Questions
People also ask.
What is the difference between a probability tree and a decision tree?
A probability tree shows only chance events, while a decision tree also includes choices the decision maker controls.
How do you solve a decision tree?
Start from the ends of the branches, calculate values, and step back to each decision point choosing the best expected value.
When should a tree not be used?
When the outcomes cannot be described, or when the probabilities are too uncertain to be useful, in which case other methods such as scenario analysis may be better. A very large tree can also become too complicated to explain.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%