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    como se le llama al cociente de eventos favorables entre eventos totales

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    Probabilidad

    Probabilidad

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    La probabilidad es una medida de la certidumbre de que ocurra un evento. Su valor es un número entre 0 y 1, donde un evento imposible corresponde a cero y uno seguro corresponde a uno.

    Una forma empírica de estimar la probabilidad consiste en obtener la frecuencia con la que sucede un determinado acontecimiento mediante la repetición de experimentos aleatorios, bajo condiciones estables. En algunos experimentos de los que se conocen todos los resultados posibles, la probabilidad de estos sucesos pueden ser calculadas de manera teórica, especialmente cuando todos son igualmente probables.

    La teoría de la probabilidad es la rama de la matemática que estudia los experimentos o fenómenos aleatorios. Se usa extensamente en áreas como la estadística, la física, las ciencias sociales, la Investigación médica, las finanzas, la economía y la filosofía para conocer la viabilidad de sucesos y la mecánica subyacente de sistemas complejos.

    Índice

    1 Terminología de la teoría de la probabilidad

    2 Interpretaciones 3 Etimología 4 Historia 5 Teoría

    5.1 Regla de la adición

    5.2 Regla de la multiplicación

    5.3 Regla de Laplace

    5.4 Distribución binomial

    6 Aplicaciones

    6.1 Investigación biomédica

    7 Relación con el azar y la probabilidad en la mecánica cuántica

    8 Véase también 9 Referencias 10 Bibliografía 11 Enlaces externos

    Terminología de la teoría de la probabilidad[editar]

    Probabilidades de lanzar varios números con dos dados.

    Experimento: Una operación que puede producir algunos resultados bien definidos pero que no se puede predecir cuál de ellos se obtendrá, se llama un experimento aleatorioEjemplo: Cuando se lanza una moneda, se sabe que solo puede aparecer cara o cruz. Sin embargo no se puede predecir al momento de lanzar la moneda en cuál lado caerá.Ejemplo: Cuando se lanza un dado se sabe que en la cara superior puede aparecer cualquiera de los números 1,2,3,4,5, o 6 pero no se puede predecir cuál aparecerá.

    Resultado: Cualquier elemento posible del espacio muestral S de un experimento aleatorio se llama Resultado.

    Suceso: Cualquier subconjunto del espacio muestral S se llama un Evento (denotado por E). Cuando se produce un resultado que pertenece al subconjunto E, se dice que ha ocurrido un suceso. Mientras que, cuando un resultado que no pertenece al subconjunto E tiene lugar, el Evento no ha ocurrido.

    Ensayo: Por ensayo, se entiende la realización de un experimento aleatorio.

    Ejemplo: (i) Lanzar una moneda , (ii) lanzar un dado imparcial1​

    Interpretaciones[editar]

    Cuando se trata de experimentos que son aleatorios y bien definidos en un entorno puramente teórico (como lanzar una moneda justa), la probabilidad puede describirse numéricamente por el número de resultados deseados, dividido por el número total de todos los resultados. Por ejemplo, si se lanza una moneda al aire dos veces, se obtendrán resultados de "cara-cara", "cara-cruz", "cruz-cara" y "cruz-cruz". La probabilidad de obtener un resultado de "cara-cara" es 1 de cada 4 resultados, o, en términos numéricos, 1/4, 0,25 o 25%. Sin embargo, en lo que respecta a la aplicación práctica, existen dos grandes categorías de interpretaciones de la probabilidad que compiten entre sí, y cuyos partidarios mantienen puntos de vista diferentes sobre la naturaleza fundamental de la probabilidad:

    Objetivistas asignan números para describir algún estado de cosas objetivo o físico. La versión más popular de la probabilidad objetiva es la probabilidad frecuentista, que afirma que la probabilidad de un evento aleatorio denota la del resultado de un experimento cuando este se repite indefinidamente. Esta interpretación considera que la probabilidad es la frecuencia relativa "a largo plazo" de los resultados. 2​ Una modificación de esto es la probabilidad de propensión, que interpreta la probabilidad como la tendencia de algún experimento a producir un determinado resultado, incluso si se realiza solo una vez.

    Los subjetivistas asignan números por probabilidad subjetiva, es decir, como un grado de creencia.3​ El grado de creencia se ha interpretado como "el precio al que se compraría o vendería una apuesta que paga 1 unidad de utilidad si E, 0 si no E. "4​ La versión más popular de la probabilidad subjetiva es la probabilidad bayesiana, que incluye el conocimiento de los expertos así como datos experimentales para calcular probabilidades. El conocimiento experto está representado por alguna distribución de probabilidad a priori (subjetiva). Estos datos se incorporan a una función de verosimilitud. El producto de la función a priori y la función de verosimilitud, cuando se normaliza, da lugar a una probabilidad a posteriori que incorpora toda la información conocida hasta la fecha.5​ Por el teorema de la concordancia de Aumann, los agentes bayesianos cuyas creencias a priori son similares terminarán con creencias posteriores similares. Sin embargo, unas creencias previas suficientemente diferentes pueden llevar a conclusiones diferentes, independientemente de la cantidad de información que compartan los agentes.6​

    Etimología[editar]

    Artículo principal:

    La palabra probabilidad deriva del latín , que también puede significar "probidad", una medida de la autoridad de un testigo en un caso legal en Europa, y a menudo correlacionada con la nobleza del testigo. En cierto sentido, esto difiere mucho del significado moderno de probabilidad, que en cambio es una medida del peso de la evidencia empírica, y se llega a ella a partir del razonamiento inductivo y la inferencia estadística.7​

    fuente : es.wikipedia.org

    Probabilidad: Cálculo

    Dili Seçin​▼

    Cálculo o medición de la Probabilidad

    La probabilidad mide la mayor o menor posibilidad de que se dé un determinado resultado (suceso o evento) cuando se realiza un experimento aleatorio.

    Para calcular la probabilidad de un evento se toma en cuenta todos los casos posibles de ocurrencia del mismo; es decir, de cuántas formas puede ocurrir determinada situación.

    Los casos favorables de ocurrencia de un evento serán los que cumplan con la condición que estamos buscando.

    La probabilidad toma valores entre 0 y 1 (o expresados en tanto por ciento, entre 0% y 100%):

    El valor cero corresponde al suceso imposible; ejemplo: lanzamos un dado al aire y la probabilidad de que salga el número 7 es cero.

    El valor uno corresponde al suceso seguro, ejemplo: lanzamos un dado al aire y la probabilidad de que salga cualquier número del 1 al 6 es igual a uno (100%).

    El resto de sucesos tendrá probabilidades entre cero y uno: que será tanto mayor cuanto más probable sea que dicho suceso tenga lugar.

    Métodos de medición de Probabilidad

    Uno de los métodos más utilizados es aplicando la Regla de Laplace: define la probabilidad de un suceso como el cociente entre casos favorables y casos posibles.

    Ejemplos: a) Probabilidad de que al lanzar un dado salga el número 2: el caso favorable (f) es tan sólo uno (que salga el dos), mientras que los casos posibles (n) son seis (puede salir cualquier número del uno al seis).

    Por lo tanto:

    (o lo que es lo mismo, 16,6%)

    b) Probabilidad de que al lanzar un dado salga un número par: en este caso los casos favorables (f) son tres (que salga el dos, el cuatro o el seis), mientras que los casos posibles (n) siguen siendo seis.

    Por lo tanto:

    (o lo que es lo mismo, 50%)

    c) Probabilidad de que al lanzar un dado salga un número menor que 5: en este caso tenemos cuatro casos favorables (f) (que salga el uno, el dos, el tres o el cuatro), frente a los seis casos posibles.

    Por lo tanto:

    (o lo que es lo mismo, 66,6%)

    d) Probabilidad de ganarse el premio mayor de una lotería en la que juegan 100.000 númerosnos: tan sólo un caso favorable (f), el número que jugamos, frente a los 100.000 casos posibles (n).

    Por lo tanto:

    (o lo que es lo mismo, 0,001%)

    d) Probabilidad al lanzar una moneda, con un águila en una cara y un sol en la otra. Hay dos casos posibles (n) de ocurrencia (o cae águila o cae sol) y sólo un caso favorable (f) de que pueda caer águila (pues sólo hay un águila en la moneda).

    Por lo tanto:

    (o, lo que es lo mismo, 50 %)

    Existe una probabilidad del 50% de obtener un águila al tirar una moneda.

    e) Probabilidad de elegir tal o cual fruta. Si en una canasta hay 20 peras y 10 manzanas. ¿Qué fruta es más probable que saque al azar de la canasta?

    Para este ejemplo tenemos que 30 es el total de frutas en la canasta; es decir los casos posibles (n). Para calcular la probabilidad de sacar una manzana los casos favorables (f) son 10 puesto que existen sólo 10 manzanas.

    Por lo tanto:

    (o, lo que es lo mismo, 33,3 %)

    (o, lo que es lo mismo, 66,7 %)

    Fíjate bien que 33,3% + 66,7% es igual al 100% porque siempre que saquemos algo de la canasta es seguro que será una fruta.

    Condiciones importantes

    Para poder aplicar la Regla de Laplace el experimento aleatorio tiene que cumplir dos requisitos:

    a) El número de resultados posibles (sucesoso eventos) tiene que ser finito. Si hubiera infinitos resultados, al aplicar la regla "casos favorables dividido por casos posibles" el cociente siempre sería cero. b) Todos los sucesos o eventos tienen que tener la misma probabilidad. Si al lanzar un dado, algunas caras tuvieran mayor probabilidad de salir que otras, no podríamos aplicar esta regla.

    A la regla de Laplace también se le denomina "probabilidad a priori", ya que para aplicarla hay que conocer antes de realizar el experimento cuales son los posibles resultados y saber que todos tienen las mismas probabilidades.

    Cuando se realiza un experimento aleatorio un número muy elevado de veces, las probabilidades de los diversos posibles sucesos empiezan a converger hacia valores determinados, que son sus respectivas probabilidades.

    Ejemplo:

    si lanzo una vez una moneda al aire y sale "cara", quiere decir que el suceso "cara" ha aparecido el 100% de las veces y el suceso "cruz" el 0%.

    Si lanzo diez veces la moneda al aire, es posible que el suceso "cara" salga 7 veces y el suceso "cruz" las 3 restantes. En este caso, la probabilidad del suceso "cara" ya no sería del 100%, sino que se habría reducido al 70%.

    fuente : www.profesorenlinea.cl

    como se le llama al cociente de eventos favorables entre eventos totales

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    fuente : brainly.lat

    ¿Quieres ver la respuesta o más?
    Santiago 4 day ago
    4

    Chicos, ¿alguien sabe la respuesta?

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