What is the sample space of a dice?

The sample space of a standard six-sided die is the collection of all possible results when the die is rolled, represented as S = {1, 2, 3, 4, 5, 6}.

Understanding Sample Space

In probability theory, the sample space (often denoted by S) is the set of all possible outcomes of a random experiment. Each individual result in the sample space is called an outcome or a sample point. Defining the sample space accurately is the fundamental first step in analyzing any probabilistic event, as it forms the basis for calculating probabilities of specific events.

The Sample Space of a Standard Die

When a standard, fair six-sided die is rolled, there are precisely six distinct possibilities for the face that lands upwards. These outcomes are inherent to the design of the die, which typically features faces numbered from one to six. On rolling a die, we can have 6 outcomes.

Listing the Outcomes

The individual outcomes when rolling a single die are the integers from 1 to 6. Therefore, the sample space for this experiment is expressed as a set:

S = {1, 2, 3, 4, 5, 6}

Here's a breakdown of each possible outcome:

This complete set represents every single result that can occur from a single roll, assuming a fair die where each face has an equal chance of landing.