Performance Management · Analytical techniques in budgeting and forecasting

Expected Values and Probability in Forecasting for ACCA PM

Updated 11 October 2026 · Fact-checked

An expected value (EV) is the weighted average of possible outcomes, using their probabilities as weights. Multiply each outcome by its probability, then add the results. The probabilities must add up to 1. EV suits repeated decisions. For a one-off decision it may not match any outcome that can actually happen.

Understand Expected Values and Probability in Forecasting

Forecasts are rarely certain. A manager may think sales could be high, medium or low, and may be able to put a probability on each. Expected value turns that spread of outcomes into one number you can use in a budget or a decision.

The idea is a weighted average. Outcomes that are more likely get more weight. If a profit of $100,000 has a probability of 0.3 and a profit of $40,000 has a probability of 0.7, the EV is (100,000 × 0.3) + (40,000 × 0.7) = $58,000. Neither outcome equals $58,000. The EV is the long-run average if the same situation could be repeated many times.

This links to risk and uncertainty. Under risk, you can assign probabilities to outcomes, so you can use EV. Under uncertainty, you cannot, so you need rules such as maximin, maximax or minimax regret.

EV is simple and uses all the outcomes. Its limits matter just as much in the exam. The probabilities are often subjective estimates. The EV may be an outcome that cannot happen. It ignores risk, because two options can have the same EV but very different spreads. It works best for repeated decisions, not one-off ones.

The difference from maximin is the attitude to risk. EV is neutral: it averages everything. Maximin is pessimistic: it picks the option whose worst outcome is the best of all the worst outcomes, and it ignores probabilities.

Key rules to remember

Expected value: EV = Σ (probability × outcome); Add the products for every possible outcome. Use the same measure throughout, such as profit or contribution.
Probability check: Σ probabilities = 1; If the probabilities do not add to 1, a case is missing or a figure is wrong. Check this before calculating.
Joint probability (independent events): P(A and B) = P(A) × P(B); Use this only when the events are independent, for example price level and an unrelated cost change.
Maximin rule: Choose the option with the highest of the minimum outcomes; Ignores probabilities. Reflects a risk-averse decision maker.
Maximax rule: Choose the option with the highest of the maximum outcomes; Ignores probabilities. Reflects an optimist or risk seeker.

How to solve Expected Values and Probability in Forecasting questions

Use this method for any expected value question, whether the numbers are profit, cost, demand or revenue.

1Read the question and note what is being measured: profit, contribution, cost or units. Decide if you must first calculate the outcome for each scenario.
2List each scenario with its probability. Check that the probabilities add to 1.
3Calculate the outcome for each scenario. Deduct fixed costs and any other relevant items where needed.
4Multiply each outcome by its probability.
5Add the products to get the EV. Do this for every option being compared.
6Choose the option with the highest EV of profit or the lowest EV of cost, if the question asks for a decision based on EV.
7Comment on limitations: subjective probabilities, a one-off decision, the EV not being a possible outcome, and risk being ignored. If asked, compare with maximin.

Quickest way: Calculate the EV directly from the scenario table

When to use it: Use this when outcomes are already given, or are simple to calculate, in a table with probabilities.

Write the probabilities down in a column and add them to check they equal 1.
Put the outcomes next to them.
Multiply across on your calculator and keep a running total using the memory key.
Round only at the end.
For a decision, put the EV of each option side by side and pick the best. Add one line on the main limitation for any written part.

Common mistakes in Expected Values and Probability in Forecasting

Using probabilities that do not add to 1, or using percentages without converting them.
Students rush to multiply and never check the data.
Fix: Add the probabilities first. Convert percentages to decimals, so 25% becomes 0.25.
Calculating the EV of units and then working out profit from that EV in a way that gives the wrong answer when profit is not a straight line of units.
Students assume it makes no difference.
Fix: If the relationship is linear, it gives the same answer. If there are steps, tiers or discounts, calculate the profit for each scenario first, then the EV of profit.
Forgetting fixed costs or other relevant items when calculating profit for each scenario.
Students stop at contribution.
Fix: Check whether the question asks for profit or contribution. Deduct fixed costs from each scenario's contribution if profit is required.
Saying the EV is the most likely outcome or the outcome that will happen.
Students confuse an average with a prediction.
Fix: Say it is a long-run weighted average. It may not be a value that can actually occur.
Applying probabilities when using maximin or maximax.
Students mix up the decision rules.
Fix: Maximin and maximax ignore probabilities. Only EV uses them.
Listing limitations without linking them to the scenario.
Students learn a generic list.
Fix: Tie each point to the case, for example that a single launch is a one-off decision, so the average may never be achieved.

Worked examples

Example 1

A company is deciding between Product X and Product Y. Product X: profit of $80,000 (probability 0.2), $50,000 (0.5) or $20,000 (0.3). Product Y: profit of $90,000 (probability 0.3), $45,000 (0.3) or $10,000 (0.4). Calculate the EV of each product and state which has the higher EV.

Show the solution

Check probabilities. X: 0.2 + 0.5 + 0.3 = 1. Y: 0.3 + 0.3 + 0.4 = 1.
EV of X = (80,000 × 0.2) + (50,000 × 0.5) + (20,000 × 0.3) = 16,000 + 25,000 + 6,000 = $47,000.
EV of Y = (90,000 × 0.3) + (45,000 × 0.3) + (10,000 × 0.4) = 27,000 + 13,500 + 4,000 = $44,500.
Compare: 47,000 is higher than 44,500.

Answer: Product X has the higher EV of profit ($47,000 against $44,500).

Example 2

Using the data in the previous example, state which product maximin would choose. Explain why this differs from the EV choice, and give two limitations of EV.

Show the solution

Find the worst outcome for each product. X: $20,000. Y: $10,000.
Maximin picks the highest of these worst outcomes. $20,000 is higher than $10,000, so Product X is chosen.
Here both methods choose X, so they do not differ in this case. They can differ in general: EV uses probabilities and averages all outcomes, while maximin ignores probabilities and looks only at the worst case.
Limitation 1: the probabilities are usually subjective estimates, so an error in them changes the EV.
Limitation 2: the EV is an average and may not be a possible outcome. For a one-off decision the company will earn $80,000, $50,000 or $20,000 from X, never $47,000. EV also ignores the spread of outcomes, so it does not show the risk.

Answer: Maximin chooses Product X, the same as EV in this case. EV is risk neutral and uses probabilities; maximin is pessimistic and ignores them. EV limitations include subjective probabilities, being a poor guide for one-off decisions and ignoring risk.

Exam tips

In Section A and OT cases, check that probabilities sum to 1 before you multiply. Questions are all or nothing, so one wrong figure loses the whole mark.
Read whether the question asks for EV of profit, contribution or revenue. Build the right measure for each scenario first.
For written parts in Section C, give a limitation and then tie it to the scenario. A generic list earns fewer marks.
When a question asks you to compare EV with maximin, state the attitude to risk behind each rule and note that maximin ignores probabilities.
Show the working in a table of probability, outcome and product. It is easy for a marker to follow and easy for you to check.

Practice questions from Analytical techniques in budgeting and forecasting

Expected Values and Probability in Forecasting in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Expected Values and Probability in Forecasting: frequently asked questions

How do I calculate the expected value of profit?

Work out the profit for each possible scenario. Multiply each profit by its probability and add the results. The probabilities must total 1.

What are the limitations of expected values?

The probabilities are often subjective. The EV may not be an outcome that can actually happen. It ignores the spread of outcomes, so it does not measure risk, and it is more suitable for repeated decisions than one-off ones.

What is the difference between expected value and maximin?

Expected value uses probabilities and averages all outcomes, so it is risk neutral. Maximin ignores probabilities and picks the option with the best worst-case outcome, so it is cautious. Use EV when probabilities are available and maximin under uncertainty.

Should I choose the highest EV for a one-off decision?

Not automatically. The EV is a long-run average, and a one-off decision will give just one outcome. Consider the range of results and the decision maker's attitude to risk as well.