Small-business owners cannot always rely on hunches, instincts and lucky guesses to survive and thrive. In a competitive business environment, the mathematical tools offered in probability analysis can show entrepreneurs the most likely outcomes and most profitable paths. Probability analysis features formulas that business owners can employ in a controlled manner to anticipate potential results. Probability distributions is one such formula.

## Probability Distribution

A probability distribution is a statistical function that identifies all the conceivable outcomes and odds that a random variable will have within a specific range. This range is determined by the lowest and highest potential values for that variable. For instance, if a company expects to bring in between \$100,000 and \$500,000 in monthly revenue, the graph will start with \$100,000 at the low end and \$500,000 at the high end. The graph for a typical probability distribution resembles a bell curve, where the least likely events fall closest to the extreme ends of the range and the most likely events occur closer to the midpoint of the extremes.

## Sales Predictions

A major application for probability distributions lies in anticipating future sales incomes. Companies of all sizes rely on sales forecasts to predict revenues, so the probability distribution of how many units the firm expects to sell in a given period can help it anticipate revenues for that period. The distribution also allows a company to see the worst and best possible outcomes and plan for both. The worst outcome could be 100 units sold in a month, while the best result could be 1,000 units sold in that month.

## Risk Assessments

Probability distributions can help companies avoid negative outcomes just as they help predict positive results. Statistical analysis can also be useful in analyzing outcomes of ventures that involve substantial risks. The distribution shows which outcomes are most likely in a risky proposition and whether the rewards for taking specific actions compensate for those risks. For instance, if the probability analysis shows that the costs of launching a new project is likely to be \$350,000, the company must determine whether the potential revenues will exceed that amount to make it a profitable venture.

## Scenario Analysis

Probability distributions are highly useful in producing tools to evaluate various business scenarios. Scenario analysis employs probability distributions to show numerous distinct possible outcomes stemming from a specific action or consequence. This analysis often involves examining the worst-case, best-case and most likely scenarios given the probability distribution for that action. For instance, the probability distribution can show that the most likely scenario for a new product launch will cost \$250,000, while the best possible scenario shows it will cost \$150,000 and the worst possible scenario shows it will cost \$500,000. Businesses can work toward the best possible outcome while preparing for the worst.