In probability theory , the complement of any event A is the event [not A ], i.e. the event that A does not occur. The event A and its complement [not A ] are mutually exclusive and exhaustive . Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A . The complement of an event A is usually denoted as A′ , A , ¬ {\displaystyle \neg } A or A . Given an event, the event and its complementary event define a Bernoulli trial : did the event occur or not?
15-544: [REDACTED] Look up complement or complementary in Wiktionary, the free dictionary. Not to be confused with compliment , an expression of praise. Complement may refer to: The arts [ edit ] Complement (music) , an interval that, when added to another, spans an octave Aggregate complementation , the separation of pitch-class collections into complementary sets Complementary color , in
30-494: A cascade of proteins in the blood that form part of innate immunity Complementary DNA , DNA reverse transcribed from a mature mRNA template Complementarity (molecular biology) , a property whereby double stranded nucleic acids pair with each other Complementation (genetics) , a test to determine if independent recessive mutant phenotypes are caused by mutations in the same gene or in different genes Grammar and linguistics [ edit ] Complement (linguistics) ,
45-455: A good often consumed together with another good Ship's complement, the number of persons in a ship's company See also [ edit ] Complementarity (disambiguation) Compliment (disambiguation) Complimentary (disambiguation) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Complement . If an internal link led you here, you may wish to change
60-455: A good often consumed together with another good Ship's complement, the number of persons in a ship's company See also [ edit ] Complementarity (disambiguation) Compliment (disambiguation) Complimentary (disambiguation) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Complement . If an internal link led you here, you may wish to change
75-564: A graph which is isomorphic to its complement Complemented lattice Geometry [ edit ] Complementary angles Knot complement Complement of a point, the dilation of a point in the centroid of a given triangle, with ratio −1/2 Logic [ edit ] Complement (set theory) Complementary event in probability Logical complement Bitwise complement Complements in boolean algebra Other uses [ edit ] Complementary experiments , in physics Complement good (economics),
90-564: A graph which is isomorphic to its complement Complemented lattice Geometry [ edit ] Complementary angles Knot complement Complement of a point, the dilation of a point in the centroid of a given triangle, with ratio −1/2 Logic [ edit ] Complement (set theory) Complementary event in probability Logical complement Bitwise complement Complements in boolean algebra Other uses [ edit ] Complementary experiments , in physics Complement good (economics),
105-845: A word or phrase having a particular syntactic role Subject complement , a word or phrase adding to a clause's subject after a linking verb Phonetic complement Complementary , a type of opposite in lexical semantics (sometimes called an antonym) Mathematics [ edit ] Algebra [ edit ] Complement (group theory) Complementary subspaces Orthogonal complement Schur complement Algorithms [ edit ] Complement (complexity) , relating to decision problems and complexity classes Complement operator (regular expressions) Method of complements , in computer science Radix complement Diminished radix complement Ones' complement Two's complement Discrete mathematics [ edit ] Complement graph Self-complementary graph ,
120-433: Is logically equivalent to [not tails], and [tails] is equivalent to [not heads]. In a random experiment , the probabilities of all possible events (the sample space ) must total to 1— that is, some outcome must occur on every trial. For two events to be complements, they must be collectively exhaustive , together filling the entire sample space. Therefore, the probability of an event's complement must be unity minus
135-402: Is tossed and one assumes that it cannot land on its edge, then it can either land showing "heads" or "tails." Because these two outcomes are mutually exclusive (i.e. the coin cannot simultaneously show both heads and tails) and collectively exhaustive (i.e. there are no other possible outcomes not represented between these two), they are therefore each other's complements. This means that [heads]
150-459: The free dictionary. Not to be confused with compliment , an expression of praise. Complement may refer to: The arts [ edit ] Complement (music) , an interval that, when added to another, spans an octave Aggregate complementation , the separation of pitch-class collections into complementary sets Complementary color , in the visual arts Biology and medicine [ edit ] Complement system (immunology),
165-485: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Complement&oldid=1238254555 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages complement [REDACTED] Look up complement or complementary in Wiktionary,
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#1732790361658180-400: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Complement&oldid=1238254555 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Complementary event For example, if a typical coin
195-401: The probability of the event. That is, for an event A , Equivalently, the probabilities of an event and its complement must always total to 1. This does not, however, mean that any two events whose probabilities total to 1 are each other's complements; complementary events must also fulfill the condition of mutual exclusivity . Suppose one throws an ordinary six-sided die eight times. What
210-960: The same gene or in different genes Grammar and linguistics [ edit ] Complement (linguistics) , a word or phrase having a particular syntactic role Subject complement , a word or phrase adding to a clause's subject after a linking verb Phonetic complement Complementary , a type of opposite in lexical semantics (sometimes called an antonym) Mathematics [ edit ] Algebra [ edit ] Complement (group theory) Complementary subspaces Orthogonal complement Schur complement Algorithms [ edit ] Complement (complexity) , relating to decision problems and complexity classes Complement operator (regular expressions) Method of complements , in computer science Radix complement Diminished radix complement Ones' complement Two's complement Discrete mathematics [ edit ] Complement graph Self-complementary graph ,
225-477: The visual arts Biology and medicine [ edit ] Complement system (immunology), a cascade of proteins in the blood that form part of innate immunity Complementary DNA , DNA reverse transcribed from a mature mRNA template Complementarity (molecular biology) , a property whereby double stranded nucleic acids pair with each other Complementation (genetics) , a test to determine if independent recessive mutant phenotypes are caused by mutations in
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