An outcome is one possible result of a random experiment. A coin flip can produce heads or tails; a roll of one die can produce any face from 1 through 6. An event specifies which outcomes count for the question at hand. If heads is the desired result, heads is both a possible outcome and the outcome that makes the event occur. section 2.1 section 3.2.3
For equally likely outcomes, probability is the number of favorable outcomes divided by the total number of possible outcomes. Define both counts before calculating: a result labeled “success” might be a product malfunction if malfunctions are what you need to track. Do not use the simple counting ratio without the equal-likelihood assumption. section 2.1 section 3.2.3
Two dice: preserve the order
Rolling two six-sided dice gives 6 × 6 = 36 ordered outcomes. The outcome (3, 4) differs from (4, 3) because the first and second dice have different results. If success means 1, 2, or 3 on the first die and 4, 5, or 6 on the second, there are 3 × 3 = 9 favorable outcomes, giving 9/36 = 0.25 under the fair-dice assumption. section 3.2.3
The same idea supports simulation and decisions, but an outcome has a different role in each:
- In a Monte Carlo simulation, assign possible outcomes probabilities, convert them to cumulative intervals, and map generated random numbers to those intervals. Repeated trials produce possible system outcomes; the chosen distribution and its parameters determine what the trials represent. section 9.2
- In a decision tree, branches from a chance node represent possible outcomes with associated probabilities. Following each branch to its payoff shows how uncertainty affects a choice; the tree is a decision aid, not a fitted classification model. section 10.2
