[b][color=#980000][size=200][size=150]El truco[/size][/size][br][/color][/b][br][size=100][size=150]Un mago solicita una persona voluntaria. Le entrega una calculadora y le indica que vaya multiplicando cifras al azar. Después de unas cuantas multiplicaciones le pide que contemple el número obtenido, que escoja una de sus cifras no nulas y que le vaya diciendo de una en una todas las demás.[/size][/size]
[b][color=#980000][code][/code][br][/color][/b][size=100][size=150]El mago escucha, piensa unos instantes y responde "la cifra escogida es..."[br][br][color=#980000][b]Explicación del truco[/b][br][br][/color]El mago sabe que el número es múltiplo de 9 y conoce el criterio de divisibilidad del 9.[br][br][table][tr][td]Sea N un número de n cifras. [math]N=\sum a_i10^i[/math]. Si dividimos por 9 cada uno de los sumandos de la expresión polinómica de N se tiene que [math]a_i=a_i\cdot10^i\left(mod\right)9[/math] y por lo tanto [math]\sum a_i=N\left(mod\right)9[/math] así que N es múltiplo de 9 si y solo si la suma de sus cifras es múltiplo de 9.[/td][/tr][/table][br]El mago va sumando las cifras asi que la cifra escogida será la que haga que la suma total sea múltiplo de 9.[br][br]Pero ¿por qué sabe el mago que el número es múltiplo de 9?[br][br]No tiene la certeza pero sabe que es altamente probable y se la juega. [br]¿Qué probabilidad tiene de acertar?[br][/size][/size][size=100][size=150][b][br][color=#980000]Distribución del número cifras necesarias para generar un múltiplo de 9[/color][/b][/size][br][size=150][color=#274e13][b][br]Definición de la variable[br][/b][/color][/size][br]Se multiplican sucesivamente cifras no nulas entre sí eligiéndolas al azar de forma independiente y equiprobable. El proceso se detiene en el instante en que el producto acumulado es múltiplo de 9.[br][br]Sea X la variable aleatoria " número de cifras introducidas hasta la detención del proceso". Se pretende determinar la función de probabilidad de x P(X=n) y la función de distribución [math]F\left(k\right)=P\left(X\le k\right)[/math][br][br]Empíricamente se comprueba que después de unas pocas cifras aparece un múltiplo de 9 y que las situaciones en las que hay que hacer más de 10 pulsaciones son altamente improbables. Usa esta aplicación para comprobarlo:[/size][br]
[size=150][color=#38761d][b]Exploración previa del problema[/b][/color][/size][br][br]Un número es múltiplo de 9 si contiene al menos dos factores de 3.[br][br]Se clasifican las cifras en:[br][br][list][*]Tipo A (0 factores de 3) : {1, 2, 4, 5, 7, 8}, P(A) = 6/9[br][br][/*][*]Tipo B (1 factor de 3) : {3, 6}, P(B) = 2/9[br][br][/*][*]Tipo C (2 factores de 3) P(C) = 1/9[br][br][/*][/list][br]El proceso termina al acumular dos factores de 3 por tanto tendrá que aparecer C o las combinaciones B+B o B+C[br][br][list][*][b]Caso n = 1[br][/b][br][/*][/list]Este caso es trivial P(X=1)=[math]\frac{1}{9}[/math][list][*][b]Caso n = 2[/b][/*][/list][img]data:image/png;base64,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[/img][br][br]Si sumamos las probabilidades de las 3 rutas: P(X=2) = [math]\frac{6}{9}\cdot\frac{1}{9}+\frac{2}{9}·\left(\frac{2}{9}+\frac{1}{9}\right)=\frac{2}{9}\cdot\frac{6}{9}=\frac{4}{27}[/math][list][*][b]Caso n = 3[/b][/*][/list][b][img]data:image/png;base64,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[/img][br][br][/b]Si sumamos las 5 rutas tenemos P(X=3)=[math]\frac{6}{9}\cdot\left(\frac{6}{9}\cdot\frac{1}{9}+\frac{2}{9}\cdot\left(\frac{2}{9}+\frac{1}{9}\right)\right)+\frac{2}{9}\cdot\frac{6}{9}\cdot\left(\frac{2}{9}+\frac{1}{9}\right)=\frac{3}{9}\cdot\left(\frac{6}{9}\right)^2=\frac{4}{27}[/math][br][size=100][br]En el caso n = 4 el r[/size]esultado es[math]P\left(X=4\right)=\frac{4}{9}\left(\frac{6}{9}\right)^3[/math] . El patrón está claro,asi que ya podríamos inducir la fórmula general.[b][br][br][br]Cálculo por tipo de ruta[/b][b][br][br]Ruta 1[/b] (terminación directa):[br][br]En los primeros n − 1 pasos todos son A. En el paso n aparece C.[br][br]La probabilidad de la ruta 1 es: [math]\left(\frac{6}{9}\right)^{n-1}\cdot\frac{1}{9}[/math][b][br][br]Ruta 2 [/b](acumulación):[br][br]En los primeros n − 1 pasos aparece exactamente un B y el resto son A. En el paso n aparece B o C.[br][br]Hay n-1 formas de intercalar un solo B en n-1 pasos así que la probabilidad de la ruta 2 es: [br][br][math]\left(\frac{6}{9}\right)^{n-2}\cdot\left(n-1\right)\frac{2}{9}\cdot\left(\frac{2}{9}+\frac{1}{9}\right)[/math][br][br][b][color=#38761d]Conclusiones[/color][/b][br][br]Si sumamos las probabilidades de ambos tipos de ruta llegamos a la función de probabilidad de la variable aleatoria:[br][br][math]P\left(X=n\right)=\frac{n}{9}\left(\frac{6}{9}\right)^{n-1}[/math][br][br]Que es el patrón que habíamos observado en el proceso inductivo,[br][br]Para obtener la función de distribución tenemos que sumar los términos de una sucesión aritmético - geométrica. El resultado es este: [br][br][br][img]data:image/png;base64,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[/img][br]Si el mago le dice a la persona que maneja la calculadora, "no uses el 1 porque ya sabes lo que pasa cuando multiplicas por 1" entonces las probabilidades de generar múltiplo de 9 aumentan. Las funciones de probabilidad y de distribución en este caso son estas:[br][br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br]En la siguiente aplicación puedes calcular las probabilidades en ambas modalidades de la variable aleatoria. 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