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In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space.[1]

For the experiment where we flip a coin twice, the four possible outcomes that make up our sample space are (H, T), (T, H), (T, T) and (H, H), where "H" represents a "heads", and "T" represents a "tails". Outcomes should not be confused with events, which are sets (or informally, "groups") of outcomes. For comparison, we could define an event to occur when "at least one 'heads'" is flipped in the experiment—that is, when the outcome contains at least one 'heads'. This event would contain all outcomes in the sample space except the element (T, T).

Sets of outcomes: events

Main article: Event (probability theory)

Since individual outcomes may be of little practical interest, or because there may be prohibitively (even infinitely) many of them, outcomes are grouped into sets of outcomes that satisfy some condition, which are called "events." The collection of all such events is a sigma-algebra.

An event containing exactly one outcome is called an elementary event. The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events.

Typically, when the sample space is finite, any subset of the sample space is an event (i. e. all elements of the power set of the sample space are defined as events).

Probability of an outcome

Outcomes may occur with probabilities that are between zero and one (inclusively). In a discrete probability distribution whose sample space is finite, each outcome is assigned a particular probability. In contrast, in a continuous distribution, individual outcomes all have zero probability, and non-zero probabilities can only be assigned to ranges of outcomes.

Equally likely outcomes

In some sample spaces, it is reasonable to estimate or assume that all outcomes in the space are equally likely (that they occur with equal probability). For example, when tossing an ordinary coin, one typically assumes that the outcomes "head" and "tail" are equally likely to occur. An implicit assumption that all outcomes are equally likely underpins most randomization tools used in common games of chance (e.g. rolling dice, shuffling cards, spinning wheels, drawing lots, etc.).

Outcomes in Asphalt games

An outcome in an Asphalt game is typically the result of a random process such as

Most of these random processes are disguised as "real-world" processes with assumed equally likely outcomes, for example the simulated spinning wheel in Asphalt 8 daily ads and Festival Special or the design of box content as cards which implies that they have somehow been shuffled.

In reality, the outer appearance of these random processes is deliberately used to induce a fallacy. None of the above-mentioned outcomes are equally likely. Each outcome is governed by secretly assigned probabilities that have nothing to do with the results of the real-world counterparts of the simulated randomization tools.

See also

References

  1. Albert, Jim (1998-01-21). Listing All Possible Outcomes (The Sample Space). Bowling Green State University. Retrieved on 2020-02-04.
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