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Cálculo de la probabilidad

La probabilidad es un área de las matemáticas que busca determinar qué tan posible es obtener un resultado aleatorio en condiciones especificas.

La probabilidad surge de estudiar y analizar eventos donde el resultado es incierto; por ejemplo, si se lanza un dado al aire, es muy probable que caiga al suelo pero, no se puede asegurar cuál cara quedará hacia arriba. En algunos casos hay un resultado más favorable que otros. Los sucesos que no cuentan con 100%de probabilidad de ocurrencia son llamados aleatorios.

Para predecir un resultado se realizan experimentos aleatorios, los cuales determinan si un suceso es poco o altamente probable. El espacio muestral (S) se define como el conjunto de todos los resultados posibles de un suceso.

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ft\left\{\left\left\{\left\left\left\left\{\left\left\{\left\left\left\left\left\{\left\{\left\left\left\left\{\left\left\left\{\left\left\left\left\{\left\left\left\{\left\left\{\left\left\left\{\left\left\left\left\left\left\{\left\left\left\left\{\left\left\{\left\left\left\left\left\left\{\left\left\left\left\left\{\left\left\left\{\left\left\left\left\left\left\left\{\left\left\left\left\{\left\left\left\{\left\left\left\left\left\left\left\{\left\left\left\left\left\left\left\{\left\left\left\left\left\left\{\left\left\left\left\left\{\left\left\left\left\left\left\left\left\left\{\left\left\left\left\left\left\left\left\left\{\left\left\left\left\left , resultado 2, ..., resultado n}

Ejemplo 1

Dos companeros lanzan un dado de seis caras al aire para jugar a pares e impares. Se desea conocer quién tiene mayor probabilidad de ganar.

Solución

Para determinar quién tiene la mayor probabilidad de obtener un resultado favorable, se define el espacio muestral:

S=\{1,2,3,4,5,6\} , donde 1, 2,3, 4,5y6son los resultados posibles.

Los eventos o sucesos de interés son:

Que sea par \left(\mathrm{A}\right)=\left\{2,4,6\right\}

Que sea impar \left(\mathbf{B}\right)=\left\{1,3,5\right\}

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