Probability - Experiment Terms

Chance Experiment

An activity which produces different results which occur randomly. An example of this would be rolling a fair 6 sided die, as the die will produce different and random results.

Trials

When an experiment is performed repeatedly, and each occurrence is considered as one. For example, rolling a die 50 times would be considered as 50 trials.

Outcome

A possible result which occurs from an experiment. An example of this would be rolling a 5, therefore 5 is considered as an outcome.

Equally Likely Outcomes

When two or more outcomes have the same chance of occurring. An example of this would be rolling a 6 and rolling a 5 on a 6 sided die, as they both have a 1/6 chance of occurring.

Sample Space

A set of all possible outcomes. They are written inside braces. For example, the Sample Space of a die would be {1, 2, 3, 4, 5, 6}.

Event

One outcome or a collection of outcomes, which are a subset of the sample space. An example of this would be rolling a 2, and rolling an even number on a die. The subjective sample space of these numbers would be {2, 4, 6}

Compound Event

A collection of two or more outcomes. An example of this would be rolling an even number on a die. The results of this would be considered as a compound event because there are more than two outcomes which fit the scenario.

Mutually Exclusive Events

Two or more events which are very mutually exclusive, meaning that they are impossible. An example of this would be rolling a 5 and rolling an even number. This means that it is impossible, as 5 is not an even number and it is an odd number.

Non-Mutually Exclusive Events

Events which share one or more outcomes. An example of this would be rolling a 5 and rolling an odd number, as this scenario is possible and can happen. The word exclusive means separated, so non-separated is this one meaning that there is a mutual connection and separated means that there isn’t a mutual connection.

Complementary Events

All the outcomes which are not included in an event. An example of this would be rolling a 2 or a 3, or rolling a 1, 4, 5 or 6. Another example is that you pass a test, or you don’t. It is basically the opposite or the two possible events which could happen, which is why it is called ‘complimentary’.