List outcomes of chance experiments
Theory
The outcomes of a chance experiment are all the separate results it can finish on. Listing every outcome is the first step; an event is then made from one or more of those outcomes.
An outcome is one of the ways a chance experiment can end.
Listing every outcome shows the whole sample of possibilities. When each outcome has the same chance, they are equally likely.
An event is made up of one or more outcomes. For a die, the event “an even number” is made of the outcomes \(2\), \(4\) and \(6\).
Different experiments have different lists of outcomes.
| Experiment | Outcomes | How many |
|---|---|---|
| Toss a coin | heads, tails | \(2\) |
| Roll a die | \(1, 2, 3, 4, 5, 6\) | \(6\) |
| Spin the spinner | red, blue, green, yellow | \(4\) |
How to list outcomes
- Look at the experiment: what can it finish on?
- Name every possible result, one by one, so none is missed.
- Check whether the outcomes are equally likely, then pick out the ones that make up an event.
A coin has two faces, and one toss lands on one of them.
Outcomes: heads, tails \((2\) outcomes\()\).
Each face is one outcome.
Outcomes: \(1, 2, 3, 4, 5, 6\) \((6\) outcomes\()\).
The arrow stops in one sector.
Outcomes: red, blue, green, yellow — all equally likely.
Keep only the even faces.
Event: \(2, 4, 6\) — three of the six outcomes.
Common pitfalls
Frequently asked questions
What is an outcome?
An outcome is one of the ways a chance experiment can finish. Tossing a coin has two outcomes: heads and tails.
What is the difference between an outcome and an event?
An outcome is a single result. An event is made of one or more outcomes, such as “an even number” on a die, which is \(2, 4, 6\).
What does equally likely mean?
Outcomes are equally likely when each has the same chance, such as the four equal sectors of a spinner.
Does a repeated colour count twice?
No. If two sectors are the same colour, that colour is listed once as an outcome; it just has a bigger chance of coming up.