In statistics and probability, an outcome is a possible result of an experiment or trial.
Defining an Outcome
Based on the provided reference, in probability theory, an outcome is a possible result of an experiment or trial. Each potential outcome arising from a specific experiment is distinct, and different outcomes are mutually exclusive. This means that for any single trial of an experiment, only one outcome can occur.
Understanding outcomes is fundamental because they form the building blocks of probability. The collection of all possible outcomes of an experiment is known as the sample space (often denoted by S or $\Omega$).
Key Characteristics of Outcomes
- Possible Result: An outcome must be a result that can happen during the experiment.
- Unique: Each outcome is distinct from other outcomes. For instance, getting a 'Heads' is different from getting a 'Tails' when flipping a coin.
- Mutually Exclusive: Only one outcome can occur per trial. If you flip a coin, you get either Heads or Tails, not both simultaneously.
Examples of Outcomes
Let's look at some common experiments and their possible outcomes:
Table of Outcomes and Sample Spaces
| Experiment | Possible Outcomes | Sample Space (S) | Number of Outcomes |
|---|---|---|---|
| Flipping a coin | Heads, Tails | {Heads, Tails} | 2 |
| Rolling a standard die | 1, 2, 3, 4, 5, 6 | {1, 2, 3, 4, 5, 6} | 6 |
| Drawing a card from a deck | Ace of Spades, 2 of Spades, ..., King of Clubs | All 52 cards | 52 |
| Flipping two coins | HH, HT, TH, TT | {HH, HT, TH, TT} | 4 |
Practical Insights
- Identifying all possible outcomes is the first step in calculating probabilities.
- The probability of a specific outcome is the number of ways that outcome can occur divided by the total number of possible outcomes (assuming equally likely outcomes).
- Complex events are made up of one or more outcomes. For example, the event "rolling an even number" on a die consists of the outcomes {2, 4, 6}.
In essence, outcomes are the specific, atomic results you can observe when you perform a probabilistic experiment or trial.
