Basics of probability

Define trials and events and connect outcomes and relative frequencies with probability.

Meaning

Probability describes how likely an event is in a specified experiment, using a number between 0 and 1. When outcomes are equally likely, divide the number of favorable outcomes by the total number of outcomes.

Example

When a fair six-sided die is rolled once, the outcomes greater than 4 are 5 and 6, so their probability is The six equally likely outcomes have total probability 1, so each has probability The distinct outcomes 5 and 6 cannot occur together in one roll, so add their probabilities: 2×=If outcomes are not equally likely, a simple ratio of counts does not give the probability. The relative frequency in a short run need not equal the probability either.

Practice for this concept

Scope and references

Topics

Trials, sample spaces, events, probability, relative frequency

Learning goal

Define trials and events and connect outcomes and relative frequencies with probability.

Helpful background

Review counting outcomes and expressing ratios.

Basic probability

These choice exercises calculate or judge specified finite data, trials, or assumptions. They do not establish data collection, written inference, model validation, or mastery of the whole statistics area.

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