Outcome (probability)

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Part of a series on statistics
Probability theory
For other uses, see Outcome.

In

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.[2]

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

sigma-algebra.[3]

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.[4]

Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the

real number). So, when defining a probability space
it is possible, and often necessary, to exclude certain subsets of the sample space from being events.

Probability of an outcome

Outcomes may occur with probabilities that are between zero and one (inclusively). In a

continuous
distribution, individual outcomes all have zero probability, and non-zero probabilities can only be assigned to ranges of outcomes.

Some "mixed" distributions contain both stretches of continuous outcomes and some discrete outcomes; the discrete outcomes in such distributions can be called atoms and can have non-zero probabilities.[5]

Under the

σ-algebra
on and not necessarily the full power set.

Equally likely outcomes

Flipping a coin leads to two outcomes that are almost equally likely.
A brass tack with point downward
Up or down? Flipping a brass tack leads to two outcomes that are not equally likely.

In some

games of chance (e.g. rolling dice, shuffling cards, spinning tops or wheels, drawing lots, etc.). Of course, players in such games can try to cheat by subtly introducing systematic deviations from equal likelihood (for example, with marked cards, loaded
or shaved dice, and other methods).

Some treatments of probability assume that the various outcomes of an experiment are always defined so as to be equally likely.

thumb tack
many times and observe whether it landed with its point upward or downward, there is no symmetry to suggest that the two outcomes should be equally likely.

See also

References

  1. ^ "Outcome - Probability - Math Dictionary". HighPointsLearning. Retrieved 25 June 2013.
  2. ^ Albert, Jim (21 January 1998). "Listing All Possible Outcomes (The Sample Space)". Bowling Green State University. Archived from the original on 16 October 2000. Retrieved June 25, 2013.
  3. ISBN 9780131471221
    .
  4. ISBN 978-0-486-63677-1
    .
  5. ISBN 0-387-94957-7
    .
  6. ISBN 0-13-165711-9
    .
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