Scenario Probabilities and Expected Profit

Assigning probabilities to scenarios produces a weighted average, not a promised outcome. The arithmetic is useful only when the scenarios cover the outcomes being modeled without overlap and the weights have a defensible interpretation. A precise-looking average cannot make unsupported assumptions more reliable. Label judgmental weights clearly when they are planning choices rather than estimates derived from data.

Calculate the weighted result

Assume three hypothetical monthly outcomes: a downside loss of $6,000, a base profit of $4,000, and an upside profit of $10,000. Assign illustrative probabilities of 25%, 50%, and 25%, respectively. The weighted contributions are −$1,500, $2,000, and $2,500, producing an expected modeled profit of $3,000.

The business never earns exactly $3,000 in any of these three specified outcomes. That number summarizes the distribution; it is not a fourth forecast. The model also contains a 25% assigned probability of a loss. A positive weighted result does not erase that downside or show that the business has enough cash to withstand it.

Check the weights and scenario boundaries

Each probability must lie between 0% and 100%, and the total must equal 100% for a complete set. If weights sum to 90%, investigate the missing 10% instead of silently normalizing them. A scenario labeled lower sales and another labeled supplier delay may overlap, so they cannot automatically be treated as mutually exclusive outcomes.

If probabilities are subjective, record the evidence and the person or process that supplied them. Test how the conclusion changes under another plausible set. At 40% downside, 40% base, and 20% upside, the same outcomes produce −$2,400 + $1,600 + $2,000 = $1,200. The lower weighted result comes entirely from different assumptions about likelihood.

Preserve decision-relevant differences

Two plans can have the same expected profit while one contains a much larger potential loss or a deeper cash trough. Compare the individual outcomes, capacity requirements, and cash schedules alongside the weighted average. A one-time decision may not resemble a repeated experiment in which an average outcome becomes informative over many trials.

Avoid using this method to imply investment returns or guaranteed business earnings. It is a transparent summary of entered operating scenarios. When the available evidence cannot support probabilities, present an unweighted range and describe the conditions for each case instead. Showing uncertainty directly is more useful than assigning arbitrary precision to a forecast.

Method references: OpenStax: Mean or Expected Value. Accessed October 22, 2026. All dollar figures are hypothetical worked examples.