This tutorial will cover outcomes and events. You’ll learn about:
In probability, we define an outcome as the singular result of some random process.
Outcome
The singular result of a chance experiment.
When you roll a die, the outcome is the role of a one or a six, etc. There is only one, singular result.
Outcomes will be different based on the process:
Random Process |
Outcome |
Die rolling |
Rolling a 5 |
Flipping a coin |
Tails |
Spinning the wheel on Wheel of Fortune |
“Bankrupt” (one of the sectors on the wheel) |
There's a difference between an outcome and an event. While outcomes only have one result, events can have multiple results.
Event
An outcome or set of outcomes.
When rolling a die, while an outcome would be a five, an event could be rolling an even number. That consists of the outcomes two, four, and six.
Random Process |
Event |
Outcome |
Die rolling |
Rolling an even number |
Rolling a 2, 4, or 6 |
Flipping a coin |
Tails |
Tails |
Spinning the wheel on Wheel of Fortune |
Sector over $500 |
“Bankrupt” |
It could be that an event has one outcome in it, like with the coin flipping: an outcome would be tails, but maybe tails is also considered an event. This is an event with one outcome in it. On the Wheel of Fortune example, maybe a sector over $500-- there are several of them.
When you do the random process once, like spinning a wheel, or rolling a die, or flipping a coin, that's called a trial.
Trial
Running a chance experiment once (e.g. rolling a die, spinning a spinner, flipping a coin)
Probability is going to be defined as the likelihood of a particular event occurring when you do one version of a random process.
Probability
A number between 0 and 1 that denotes the likelihood of an event. Events with probabilities closer to 1 are more likely to occur than events with probabilities closer to 0.
A graph of probability might look like this:
The number in the center, which is 0.5, is considered neither likely nor unlikely. It's equally likely to occur as not occur.
What are some events that would fall on this spectrum, from unlikely to likely?
Some possible examples might be:
Probability theory discusses the ways to quantify likelihood. Probability is a way to determine how likely certain outcomes or events are when you run a trial of a chance experiment. There difference between outcomes and events is that outcome is the singular result of one trial, whereas an event could be many outcomes, or results, of a single trial.
Thank you and good luck!
Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS
An outcome or set of outcomes.
The singular result of a chance experiment.
A number between 0 and 1 that denotes the likelihood of an event. Events with probabilities closer to 1 are more likely to occur than events with probabilities closer to 0.
Running a chance experiment once (e.g. rolling a die, spinning a spinner, flipping a coin)