Theoretical probability computes an event’s chance from a specified model rather than from observations. It divides favorable outcomes by total possible outcomes, assuming a fixed setting with equally likely outcomes. section 2.1 section 2.5
Use the model and event structure to choose the appropriate calculation.
- Count favorable outcomes and divide by all possible outcomes. section 3.2
- Apply the multiplication rule to independent events occurring together or in sequence. section 2.5 section 3.2
- Apply the addition rule to mutually exclusive events that cannot occur simultaneously. section 2.5 section 3.2
- Distinguish theoretical probability from empirical probability, which uses observed successes divided by observations. section 2.5
Rolling a six-sided die
For an even result, three of six outcomes are favorable, so the theoretical probability is 3/6, or 50%. For a 4, it is 1/6, approximately 16.7%; the corresponding odds are 1/5, or 20%. section 3.2
