Outcomes - The Possible Results of an Experiment
An outcome is one possible result of a single trial of a probability experiment. When you roll a die, each of the numbers 1, 2, 3, 4, 5, and 6 is a separate outcome. Listing every possible outcome clearly and completely is the starting point for every probability calculation.
Elementary Outcomes
An elementary outcome (also called a simple outcome or sample point) is an individual result that cannot be broken down any further. For example, rolling a 3 on a die is a single elementary outcome – you cannot split it into smaller results.
Equally Likely Outcomes
Outcomes are equally likely when each one has exactly the same chance of occurring. A fair coin has two equally likely outcomes: Heads and Tails. A fair die has six equally likely outcomes: 1, 2, 3, 4, 5, 6. When outcomes are equally likely, theoretical probability is straightforward to calculate.
Listing Outcomes Systematically
For experiments with two or more steps, it helps to list outcomes in a systematic way to make sure none are missed. Common methods include:
- Ordered lists
- Two-way tables (grids)
- Tree diagrams (covered in a later topic)
Worked Examples
| First toss | Second toss | Outcome |
|---|---|---|
| H | H | HH |
| H | T | HT |
| T | H | TH |
| T | T | TT |
Total outcomes = 4.
Die outcomes: 1, 2, 3, 4, 5, 6. Coin outcomes: H, T. Combine each:
(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T)
Total outcomes = 6 × 2 = 12.
(R,B), (R,G), (B,R), (B,G), (G,R), (G,B) – Total = 6 outcomes.
Note: (R,R) is impossible because the ball is not replaced.
Counting Outcomes: The Multiplication Principle
If experiment A has m outcomes and experiment B has n outcomes, then doing both together has m × n outcomes. This extends to any number of experiments multiplied together.
Key Takeaways
- An outcome is one specific result of a probability experiment.
- List outcomes systematically – use tables or diagrams to avoid missing any.
- Equally likely outcomes simplify probability calculation.
- For multi-step experiments, total outcomes = product of individual outcome counts.
Practice Questions
- List all outcomes when a fair die is rolled once.
- List all outcomes when two coins are tossed at the same time.
- A spinner has sections numbered 1, 2, 3. A coin is tossed. List all combined outcomes using a table.
- How many outcomes are there when two dice are rolled simultaneously?
- A bag has 4 balls (Red, Blue, Green, Yellow). One is drawn, noted, and replaced; then a second is drawn. How many outcomes are there in total?