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条件概率 Baldintzapeko probabilitate Умовна ймовірність 条件付き確率 احتمال شرطي Voorwaardelijke kans Условная вероятность Probabilitat condicionada Prawdopodobieństwo warunkowe 조건부 확률 Bedingte Wahrscheinlichkeit Probabilidade condicionada Probabilità condizionata Probabilidad condicionada Conditional probability Probabilité conditionnelle Betingad sannolikhet
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条件付き確率(じょうけんつきかくりつ、英: conditional probability)は、ある事象 B が起こるという条件下での別の事象 A の確率のことをいう。条件付き確率は P(A|B) または PB(A) のように表される。条件付き確率 P(A|B) はしばしば「B が起こったときの A の(条件付き)確率」「条件 B の下での A の確率」などと表現される。なお英文においては通例、“probability of A given B” または “probability of A under the condition B” と表現される。 Een voorwaardelijke kans of voorwaardelijke waarschijnlijkheid is de kans op een bepaalde gebeurtenis, gegeven dat een andere gebeurtenis plaatsvindt, waardoor de mogelijke uitkomsten beperkt zijn. De voorwaardelijke kans dat een gebeurtenis plaatsvindt, gegeven dat een andere gebeurtenis plaatsvindt, wordt genoteerd als en is gedefinieerd als: met andere woorden, de verhouding van de kans dat en beide zijn opgetreden en de kans op zelf. Let op: de streep in de notatie van een voorwaardelijke kans is een rechtopstaande streep, niet een (schuine) deelstreep! في دراسة الاحتمالات، احتمال شرطي هو احتمال وقوع حدث ما علما أن حدثا آخر ما قد وقع. نفرض أن E حدث اختياري ما ضمن فضاء العينة S بحيث. عندئذ نعرف احتمال وقوع الحدث A بفرض أن E قد وقع أو بعبارة أخرى الاحتمال الشرطي للحدث Aعند وقوع E (ويكتب): Усло́вная вероя́тность — вероятность наступления события при условии, что событие произошло. Вероятность события , вычисленную в предположении, что о результате эксперимента уже что-то известно (событие произошло), мы будем обозначать через . Например, вероятность того, что у какого-то человека будет кашель в произвольный день . Но если мы знаем или предполагаем, что у человека простуда, тогда у него гораздо больше шансов начать кашлять. Таким образом, условная вероятность кашля у любого человека при условии, что он простужен, выше . La probabilitat condicionada és la probabilitat que hi hagi un succés A, sabent que també succeeix un altre succés B. La probabilitat condicional s'escriu P(A|B), i es llegeix «la probabilitat de A donada B». No cal que existeixi una relació causal o temporal entre A i B. A pot precedir en el temps a B, succeir-lo o poden ser simultanis. A pot causar B, viceversa o poden no tenir relació causal. Les relacions causals o temporals són nocions que no pertanyen a l'àmbit de la probabilitat. Poden desenvolupar un paper o no depenent de la interpretació que es doni als successos. Probabilidad condicional es la probabilidad de que ocurra un evento A, sabiendo que también sucede otro evento B. La probabilidad condicional se escribe P(A|B) o P(A/B), y se lee «la probabilidad de A dado B». Un ejemplo clásico es el lanzamiento de una moneda para luego lanzar un dado. ¿Cuál es la probabilidad de que en el dado salga un 6 si ya ha salido una cara en la moneda? Esta probabilidad se denota de esta manera: . El condicionamiento de probabilidades puede lograrse aplicando el teorema de Bayes. Умо́вна ймові́рність — ймовірність однієї події за умови, що інша подія вже відбулася. Нехай — фіксований ймовірнісний простір. Нехай дві випадкової події, причому . Тоді умовною ймовірністю події при умові події називається 本文定义了表征两个或者多个随机变量概率分布特点的术语。 条件概率(英語:conditional probability)就是事件A在事件B发生的条件下发生的概率。条件概率表示为P(A|B),读作“A在B发生的条件下发生的概率”。 联合概率表示两个事件共同发生的概率。A与B的联合概率表示为或者或者。 边缘概率是某个事件发生的概率。边缘概率是這樣得到的:在聯合概率中,把最終結果中不需要的那些事件合并成其事件的全概率而消失(對离散隨机變量用求和得全概率,對連續隨机變量用積分得全概率)。這稱為邊緣化(marginalization)。A的边缘概率表示为P(A),B的边缘概率表示为P(B)。 需要注意的是,在这些定义中A与B之间不一定有因果或者时间序列关系。A可能会先于B发生,也可能相反,也可能二者同时发生。A可能会导致B的发生,也可能相反,也可能二者之间根本就没有因果关系。 例如考虑一些可能是新的信息的概率条件性可以通过贝叶斯定理实现。 Baldintzapeko probabilitateak gertakizun bat gauzatu dela jakinda, beste gertakizun bat gertatzeko probabilitatea adierazten du. Honela izendatzen da B baldintzapeko edo B gertatu dela jakinda A-ren probabilitatea: . Honela kalkula daiteke ebakiduraren probabilitatea ezagutzen bada: A eta B gertakizunak elkarrekiko independenteak badira, B gertakizuna gauzatu izanak deus gaineratzen ez duenez A gertakizunari buruz: Bi gertakizun bateraezinak badira gainera, B gertatu bada, A ezin gerta daitekeenez: In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) or occasionally PB(A). This can also be understood as the fraction of probability B that intersects with A: . Prawdopodobieństwo warunkowe zajścia zdarzenia pod warunkiem zajścia zdarzenia (o dodatnim prawdopodobieństwie) – liczba tj. iloraz prawdopodobieństwa części wspólnej zdarzeń i oraz prawdopodobieństwa zdarzenia . Niech będzie przestrzenią probabilistyczną. Przy ustalonym zdarzeniu o dodatnim prawdopodobieństwie, prawdopodobieństwo warunkowe jest zwykłym prawdopodobieństwem na stąd bywa oznaczane czasem symbolem . Bedingte Wahrscheinlichkeit (auch konditionale Wahrscheinlichkeit) ist die Wahrscheinlichkeit des Eintretens eines Ereignisses unter der Bedingung, dass das Eintreten eines anderen Ereignisses bereits bekannt ist. Sie wird als geschrieben. Der senkrechte Strich ist als „unter der Bedingung“ zu lesen und wie folgt zu verstehen: Wenn das Ereignis eingetreten ist, beschränken sich die Möglichkeiten auf die Ergebnisse in . Damit ändert sich auch die Wahrscheinlichkeit; diese neue Wahrscheinlichkeit für das Ereignis ist gegeben durch . Die bedingte Wahrscheinlichkeit kann also als Neueinschätzung der Wahrscheinlichkeit von interpretiert werden, wenn die Information vorliegt, dass das Ereignis bereits eingetreten ist. Manchmal wird auch die Schreibweise verwendet, die jedoch auch andere Na matemática, a probabilidade condicionada refere-se à probabilidade de um evento A sabendo que ocorreu um outro evento B e representa-se por P(A|B), lida "probabilidade condicional de A dado B" ou ainda "probabilidade de A dependente da condição B". In teoria della probabilità la probabilità condizionata di un evento rispetto a un evento è la probabilità che si verifichi sapendo che è verificato. Questa probabilità, indicata o , esprime una "correzione" delle aspettative per dettata dall'osservazione di Poiché, come si vedrà nella successiva definizione, compare al denominatore, ha senso solo se ha una probabilità non nulla di verificarsi. È utile osservare che la notazione con il simbolo "barra verticale" è comune con la definizione del connettivo logico NAND. 확률론에서 조건부 확률(條件附確率, 영어: conditional probability)은 주어진 사건이 일어났을 때 다른 한 사건이 일어날 확률을 뜻한다. 원래의 확률 함수를 라고 할 때, 사건 가 일어났을 때 사건 가 일어날 조건부 확률은 로 표기한다. Betingad sannolikhet är ett uttryck från sannolikhetsläran. P(B|A) (utläses "sannolikheten för B, givet A") är den betingade sannolikheten (villkorliga sannolikheten) för B då A inträffar, alltså hur stor sannolikhet det är att B inträffar om det redan är känt att A har inträffat. Den betingade sannolikheten blir då den blårastrerade ytan genom hela ytan som är blå i någon form. Om A och B är oberoende är sannolikheten för B inte beroende av om A har inträffat eller inte, och alltså är . Detta ger sambandet: En théorie des probabilités, une probabilité conditionnelle est la probabilité d'un événement sachant qu'un autre événement a eu lieu. Par exemple, si une carte d'un jeu est tirée au hasard, on estime qu'il y a une chance sur quatre d'obtenir un cœur ; mais si on aperçoit un reflet rouge sur la table, il y a maintenant une chance sur deux d'obtenir un cœur. Cette seconde estimation correspond à la probabilité conditionnelle d'obtenir un cœur sachant que la carte est rouge.
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Conditional Probability
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ConditionalProbability
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Na matemática, a probabilidade condicionada refere-se à probabilidade de um evento A sabendo que ocorreu um outro evento B e representa-se por P(A|B), lida "probabilidade condicional de A dado B" ou ainda "probabilidade de A dependente da condição B". Baldintzapeko probabilitateak gertakizun bat gauzatu dela jakinda, beste gertakizun bat gertatzeko probabilitatea adierazten du. Honela izendatzen da B baldintzapeko edo B gertatu dela jakinda A-ren probabilitatea: . Honela kalkula daiteke ebakiduraren probabilitatea ezagutzen bada: A eta B gertakizunak elkarrekiko independenteak badira, B gertakizuna gauzatu izanak deus gaineratzen ez duenez A gertakizunari buruz: Bi gertakizun bateraezinak badira gainera, B gertatu bada, A ezin gerta daitekeenez: La probabilitat condicionada és la probabilitat que hi hagi un succés A, sabent que també succeeix un altre succés B. La probabilitat condicional s'escriu P(A|B), i es llegeix «la probabilitat de A donada B». No cal que existeixi una relació causal o temporal entre A i B. A pot precedir en el temps a B, succeir-lo o poden ser simultanis. A pot causar B, viceversa o poden no tenir relació causal. Les relacions causals o temporals són nocions que no pertanyen a l'àmbit de la probabilitat. Poden desenvolupar un paper o no depenent de la interpretació que es doni als successos. El condicionament de probabilitats pot aconseguir-se aplicant el teorema de Bayes. Betingad sannolikhet är ett uttryck från sannolikhetsläran. P(B|A) (utläses "sannolikheten för B, givet A") är den betingade sannolikheten (villkorliga sannolikheten) för B då A inträffar, alltså hur stor sannolikhet det är att B inträffar om det redan är känt att A har inträffat. Den betingade sannolikheten blir då den blårastrerade ytan genom hela ytan som är blå i någon form. Om A och B är oberoende är sannolikheten för B inte beroende av om A har inträffat eller inte, och alltså är . Detta ger sambandet: Slutsaten blir då: Om A och B är oberoende är sannolikheten för att A och B ska inträffa lika med sannolikheten för A multiplicerat med sannolikheten för B. Een voorwaardelijke kans of voorwaardelijke waarschijnlijkheid is de kans op een bepaalde gebeurtenis, gegeven dat een andere gebeurtenis plaatsvindt, waardoor de mogelijke uitkomsten beperkt zijn. De voorwaardelijke kans dat een gebeurtenis plaatsvindt, gegeven dat een andere gebeurtenis plaatsvindt, wordt genoteerd als en is gedefinieerd als: met andere woorden, de verhouding van de kans dat en beide zijn opgetreden en de kans op zelf. Let op: de streep in de notatie van een voorwaardelijke kans is een rechtopstaande streep, niet een (schuine) deelstreep! In plaats van de voorwaardelijke kans op , gegeven , wordt ook vaak gesproken van de kans op onder de voorwaarde . 확률론에서 조건부 확률(條件附確率, 영어: conditional probability)은 주어진 사건이 일어났을 때 다른 한 사건이 일어날 확률을 뜻한다. 원래의 확률 함수를 라고 할 때, 사건 가 일어났을 때 사건 가 일어날 조건부 확률은 로 표기한다. In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) or occasionally PB(A). This can also be understood as the fraction of probability B that intersects with A: . For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be 75%, in which case we would have that P(Cough) = 5% and P(Cough|Sick) = 75 %. Although there is a relationship between A and B in this example, such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously. P(A|B) may or may not be equal to P(A) (the unconditional probability of A). If P(A|B) = P(A), then events A and B are said to be independent: in such a case, knowledge about either event does not alter the likelihood of each other. P(A|B) (the conditional probability of A given B) typically differs from P(B|A). For example, if a person has dengue fever, the person might have a 90% chance of being tested as positive for the disease. In this case, what is being measured is that if event B (having dengue) has occurred, the probability of A (tested as positive) given that B occurred is 90%, simply writing P(A|B) = 90%. Alternatively, if a person is tested as positive for dengue fever, they may have only a 15% chance of actually having this rare disease due to high false positive rates. In this case, the probability of the event B (having dengue) given that the event A (testing positive) has occurred is 15% or P(B|A) = 15%. It should be apparent now that falsely equating the two probabilities can lead to various errors of reasoning, which is commonly seen through base rate fallacies. While conditional probabilities can provide extremely useful information, limited information is often supplied or at hand. Therefore, it can be useful to reverse or convert a conditional probability using Bayes' theorem: . Another option is to display conditional probabilities in conditional probability table to illuminate the relationship between events. Bedingte Wahrscheinlichkeit (auch konditionale Wahrscheinlichkeit) ist die Wahrscheinlichkeit des Eintretens eines Ereignisses unter der Bedingung, dass das Eintreten eines anderen Ereignisses bereits bekannt ist. Sie wird als geschrieben. Der senkrechte Strich ist als „unter der Bedingung“ zu lesen und wie folgt zu verstehen: Wenn das Ereignis eingetreten ist, beschränken sich die Möglichkeiten auf die Ergebnisse in . Damit ändert sich auch die Wahrscheinlichkeit; diese neue Wahrscheinlichkeit für das Ereignis ist gegeben durch . Die bedingte Wahrscheinlichkeit kann also als Neueinschätzung der Wahrscheinlichkeit von interpretiert werden, wenn die Information vorliegt, dass das Ereignis bereits eingetreten ist. Manchmal wird auch die Schreibweise verwendet, die jedoch auch andere Bedeutungen haben kann. Für einen verallgemeinerten, abstrakten Begriff von bedingten Wahrscheinlichkeiten siehe bedingter Erwartungswert. In teoria della probabilità la probabilità condizionata di un evento rispetto a un evento è la probabilità che si verifichi sapendo che è verificato. Questa probabilità, indicata o , esprime una "correzione" delle aspettative per dettata dall'osservazione di Poiché, come si vedrà nella successiva definizione, compare al denominatore, ha senso solo se ha una probabilità non nulla di verificarsi. È utile osservare che la notazione con il simbolo "barra verticale" è comune con la definizione del connettivo logico NAND. في دراسة الاحتمالات، احتمال شرطي هو احتمال وقوع حدث ما علما أن حدثا آخر ما قد وقع. نفرض أن E حدث اختياري ما ضمن فضاء العينة S بحيث. عندئذ نعرف احتمال وقوع الحدث A بفرض أن E قد وقع أو بعبارة أخرى الاحتمال الشرطي للحدث Aعند وقوع E (ويكتب): Умо́вна ймові́рність — ймовірність однієї події за умови, що інша подія вже відбулася. Нехай — фіксований ймовірнісний простір. Нехай дві випадкової події, причому . Тоді умовною ймовірністю події при умові події називається Probabilidad condicional es la probabilidad de que ocurra un evento A, sabiendo que también sucede otro evento B. La probabilidad condicional se escribe P(A|B) o P(A/B), y se lee «la probabilidad de A dado B». No tiene por qué haber una relación causal o temporal entre A y B. A puede preceder en el tiempo a B, sucederlo o pueden ocurrir simultáneamente. A puede causar B, viceversa o pueden no tener relación causal. Las relaciones causales o temporales son nociones que no pertenecen al ámbito de la probabilidad. Pueden desempeñar un papel o no, dependiendo de la interpretación que se le dé a los eventos. Un ejemplo clásico es el lanzamiento de una moneda para luego lanzar un dado. ¿Cuál es la probabilidad de que en el dado salga un 6 si ya ha salido una cara en la moneda? Esta probabilidad se denota de esta manera: . El condicionamiento de probabilidades puede lograrse aplicando el teorema de Bayes. Prawdopodobieństwo warunkowe zajścia zdarzenia pod warunkiem zajścia zdarzenia (o dodatnim prawdopodobieństwie) – liczba tj. iloraz prawdopodobieństwa części wspólnej zdarzeń i oraz prawdopodobieństwa zdarzenia . Niech będzie przestrzenią probabilistyczną. Przy ustalonym zdarzeniu o dodatnim prawdopodobieństwie, prawdopodobieństwo warunkowe jest zwykłym prawdopodobieństwem na stąd bywa oznaczane czasem symbolem . En théorie des probabilités, une probabilité conditionnelle est la probabilité d'un événement sachant qu'un autre événement a eu lieu. Par exemple, si une carte d'un jeu est tirée au hasard, on estime qu'il y a une chance sur quatre d'obtenir un cœur ; mais si on aperçoit un reflet rouge sur la table, il y a maintenant une chance sur deux d'obtenir un cœur. Cette seconde estimation correspond à la probabilité conditionnelle d'obtenir un cœur sachant que la carte est rouge. Les probabilités conditionnelles font l'objet de paradoxes tels que le paradoxe des deux enfants, le paradoxe des deux enveloppes, le paradoxe des trois pièces de monnaie et le paradoxe des prisonniers. 本文定义了表征两个或者多个随机变量概率分布特点的术语。 条件概率(英語:conditional probability)就是事件A在事件B发生的条件下发生的概率。条件概率表示为P(A|B),读作“A在B发生的条件下发生的概率”。 联合概率表示两个事件共同发生的概率。A与B的联合概率表示为或者或者。 边缘概率是某个事件发生的概率。边缘概率是這樣得到的:在聯合概率中,把最終結果中不需要的那些事件合并成其事件的全概率而消失(對离散隨机變量用求和得全概率,對連續隨机變量用積分得全概率)。這稱為邊緣化(marginalization)。A的边缘概率表示为P(A),B的边缘概率表示为P(B)。 需要注意的是,在这些定义中A与B之间不一定有因果或者时间序列关系。A可能会先于B发生,也可能相反,也可能二者同时发生。A可能会导致B的发生,也可能相反,也可能二者之间根本就没有因果关系。 例如考虑一些可能是新的信息的概率条件性可以通过贝叶斯定理实现。 条件付き確率(じょうけんつきかくりつ、英: conditional probability)は、ある事象 B が起こるという条件下での別の事象 A の確率のことをいう。条件付き確率は P(A|B) または PB(A) のように表される。条件付き確率 P(A|B) はしばしば「B が起こったときの A の(条件付き)確率」「条件 B の下での A の確率」などと表現される。なお英文においては通例、“probability of A given B” または “probability of A under the condition B” と表現される。 Усло́вная вероя́тность — вероятность наступления события при условии, что событие произошло. Вероятность события , вычисленную в предположении, что о результате эксперимента уже что-то известно (событие произошло), мы будем обозначать через . Например, вероятность того, что у какого-то человека будет кашель в произвольный день . Но если мы знаем или предполагаем, что у человека простуда, тогда у него гораздо больше шансов начать кашлять. Таким образом, условная вероятность кашля у любого человека при условии, что он простужен, выше . Очевидный частный случай: неплохо иллюстрируется шуткой «Интернет-опрос показал, что 100 % респондентов пользуются интернетом». Условная вероятность является одним из наиболее фундаментальных и одним из наиболее важных понятий теории вероятностей. Если , то события и называются независимыми, т.е наступление одного из них не изменяет вероятность наступления другого. Кроме того, в общем случае . Например, если у вас лихорадка денге (событие ), то вероятность получить положительный результат теста на лихорадку (событие ) , то есть . И, наоборот, если вы получили положительный результат теста на лихорадку денге, вероятность того, что она у вас есть всего . В этом случае произошло событие (наличие лихорадки денге) при условии события (тест положительный), то есть . При ошибочном приравнивании двух вероятностей возникают различные заблуждения, такие как ошибка базового процента. Для точного подсчета условной вероятности используют теорему Байеса.
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dbr:Brownian_excursion
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dbr:Category_utility
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dbr:Radon–Nikodym_theorem
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dbr:Randomized_algorithm
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dbr:Chain_rule_for_Kolmogorov_complexity
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dbr:Loop-erased_random_walk
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dbr:Marginal_model
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dbr:Schrödinger_method
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dbr:Sleeping_Beauty_problem
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dbr:Variable-order_Markov_model
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dbr:Neural_decoding
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dbr:Expected_utility_hypothesis
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dbr:Factor_graph
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dbr:Conditional_Probability
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dbr:Conditional_probability
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dbr:Postselection
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dbr:The_Mathematics_of_Games_and_Gambling
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dbr:Unconditional_probability
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wikipedia-en:Conditional_probability
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dbr:Conditional_probability