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