Utfallens

Utfallens, in the context of probability and statistics, refers to the individual results produced by a random experiment. An utfallet (singular) is a single possible result, while the definite plural utfallen denotes all outcomes that can occur. The complete set of all possible outcomes is called the sample space.

In probability theory, a distinction is made between an utfall and a händelse (event). A händelse is any subset of the sample space and may consist of one or more utfallen. The probability of an event is the sum of the probabilities of its constituent utfallen. For finite, equally likely utfallen, each outcome has probability 1 divided by the number of utfallen.

Examples help illustrate the concept. Rolling a fair six-sided die yields six utfallen: 1, 2, 3, 4, 5, and 6. A fair coin has two utfallen: heads and tails. Drawing one card from a standard deck provides 52 utfallen. In these finite cases, probabilities can be assigned directly to individual utfallen or to events.

In cases with continuous outcomes, such as measuring height, the probability of a single utfallet is effectively zero. Instead, probability is assigned to ranges of values, and the probability of an event corresponds to the measure of the range it covers.

Terminology notes: utfallen is Swedish for outcomes, with utfallen as the definite plural and utfallens as the possessive form. The concept is foundational for defining sample space, events, and probability calculations.