By Autumn Glenister Updated Aug 30, 2022
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Probability is the science of quantifying uncertainty. Whether you’re modeling financial risk, forecasting scientific outcomes, or setting betting odds, a clear grasp of how probability is calculated can give you a decisive advantage.
Theoretical probability—also called a priori probability—is determined mathematically before any experiment takes place. For example, when rolling two standard dice, the total number of possible outcomes is 36. Only three of these outcomes sum to four: (1,3), (2,2), and (3,1). Therefore, the theoretical probability of rolling a sum of four is 3 ÷ 36, or 1/12.
Empirical probability is derived from observed data after an event has occurred. By recording how often a particular outcome appears, we can estimate its likelihood for future events. For instance, if a coin is tossed 100 times and lands heads 48 times, the empirical probability of heads is 48/100, or 0.48. The more trials we observe, the more reliable the estimate becomes.
Subjective probability reflects personal judgment or intuition about an event’s likelihood, especially when objective data are scarce. A seasoned physician might estimate a patient’s life expectancy based on clinical experience and case studies—an approach grounded in expertise rather than pure mathematics.
Different contexts favor different probability methods. Bookmakers, for instance, rely on empirical data—past race times, jockey performance, track conditions—to set odds for horse races. In contrast, when predicting outcomes of a perfectly random process like dice rolls, theoretical probability is the appropriate tool, as each face of a fair die has an equal chance of landing upward.
Choosing the right probability framework—whether theoretical, empirical, or subjective—ensures more accurate predictions and better decision‑making across fields such as business, science, and entertainment.
