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An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?

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Answer to a math question An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?

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Lurline
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108 Answers
Para encontrar la probabilidad de que un nĂșmero entero tomado al azar de los primeros 40 enteros positivos sea divisible por 5 o 6, primero podemos contar el nĂșmero de nĂșmeros enteros en el rango dado que son divisibles por 5 o 6, y luego dividir ese recuento por nĂșmero total de nĂșmeros enteros en el rango. Primero, contemos el nĂșmero de nĂșmeros enteros en el rango de 1 a 40 que son divisibles por 5 o 6. Podemos hacerlo encontrando los mĂșltiplos de 5 y 6 dentro de este rango. Los mĂșltiplos de 5 en este rango son 5, 10, 15, 20, 25, 30, 35 y 40. Los mĂșltiplos de 6 en este rango son 6, 12, 18, 24, 30 y 36. Sin embargo, necesitamos tener cuidado de no contar dos veces los mĂșltiplos comunes de 5 y 6. Entonces, el nĂșmero total de nĂșmeros enteros en el rango que son divisibles por 5 o 6 es 14. A continuaciĂłn, calculamos la probabilidad dividiendo el nĂșmero de resultados favorables (14) por el nĂșmero total de resultados posibles (40). Por lo tanto, la probabilidad de que un nĂșmero entero tomado al azar de los primeros 40 enteros positivos sea divisible por 5 o 6 es 14/40, lo que se simplifica a 7/20 o 0,35.

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