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nadya68
18 days ago
5

A software engineer creates a LAN game where an 8 digit code made up of 1,2,3,4,5,6,7,8 has to be decided on, universal code . T

here is a condition that each number has to be used a and no number can be repeated . What is the probability that first 4 digits of the code are even numbers ?
Mathematics
1 answer:
PIT_PIT [12.4K]18 days ago
3 0

Respuesta:

0.0143 = 1.43% de probabilidad de que los primeros 4 dígitos del código sean números pares.

Explicación paso a paso:

Arreglos de elementos n:

El número de arreglos posibles de n elementos se determina por:

A_{n} = n!

Probabilidad:

La probabilidad se calcula dividiendo el número de resultados deseados por el número total de resultados.

En esta pregunta:

Resultados deseados:

Los primeros cuatro dígitos son pares (2, 4, 6 y 8 son pares, así que se consideran 4 elementos).

Los últimos cuatro dígitos son impares (1, 3, 5 y 7 son impares, por lo que los últimos cuatro elementos son también arreglos de 4 elementos). Entonces

D = 4!*4! = 24*24 = 576

Resultados totales:

Arreglos de 8 dígitos. Así que

T = A_{8} = 8! = 40320

Probabilidad:

p = \frac{D}{T} = \frac{576}{40320} = 0.0143

0.0143 = 1.43% de probabilidad de que los primeros 4 dígitos del código sean números pares.

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