How can I calculate a simple probability by counting equally likely outcomes?

Start by defining the experiment: what happens once, and what counts as one outcome? Write down the complete set of possible outcomes before choosing the ones you want. That complete set is called the sample space; the event is the subset that meets your question. For example, assume one roll of a fair six-sided number cube, with its six faces as the possible outcomes. If the event is “roll greater than 4,” the event is {5, 6}. There are 2 favorable outcomes out of 6 total, so the probability is 2/6 = 1/3. The counting rule works here because the outcomes are equally likely. [S1]

Make the outcome list match the experiment exactly. For one die roll, each face value appears once; don’t list “an odd result” as one outcome alongside individual faces, because that mixes categories with results. Check that every possible result is represented and that each appears only once. Then describe the event as a clear rule and select all results that satisfy it. For “roll greater than 4,” check each listed face against the rule: 1 through 4 do not qualify; 5 and 6 do. This gives a transparent count rather than relying on a guess. If the experiment has more steps, define whether an outcome is an ordered sequence or an unordered group before listing it.

Use this setup:

1. Experiment: one roll of a fair six-sided die.
2. Sample space: {1, 2, 3, 4, 5, 6}.
3. Event: result greater than 4 = {5, 6}.
4. Favorable outcomes: 2; total outcomes: 6.
5. Probability: 2/6 = 1/3.

The fraction 2/6 expresses the share of listed outcomes that meet the event; simplifying it gives 1/3. The same source illustrates the rule with odd results on a fair six-sided number cube: 3 of 6 outcomes are odd, or 1/2. [S1] For your own problem, replace the experiment, list, and event with your specific ones, then count. The arithmetic is only as sound as the outcome list and the equal-likelihood assumption.

Don’t use favorable-count divided by total-count unless the outcomes in your sample space are equally likely. A count alone treats every listed outcome as having the same chance, so it can mislead when that assumption does not hold. Pause and state what you know: what outcomes are possible, what makes you think their chances are equal, and what information is missing? The cited example establishes the counting rule for equally likely outcomes; it does not establish that every real-world process is fair or provide a method for assigning unequal probabilities. If equal likelihood is uncertain, keep that uncertainty visible rather than presenting the fraction as a justified probability.