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katovenus [111]
2 years ago
15

solo el 20% de los empleados de la población civil que está en una base militar restringida porta su identificación personal. Si

llegan 10 empleados, cuál es la probabilidad de que el guardia de seguridad encuentre
Mathematics
1 answer:
prisoha [69]2 years ago
3 0

Usando la distribución binomial, hay una probabilidad de 0.8926 = 89.26% de que el guardia de seguridad encuentre al menos uno en la base militar restringida.

<h3>¿Qué es la distribución binomial?</h3>

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

Los parámetros son:

  • n es el número de ensayos.
  • p es la probabilidad de éxito en un ensayo
  • x es el número de éxitos

En este problema, hay que:

  • 20% de los empleados de la población civil que está en una base militar restringida porta su identificación personal, o sea p = 0.2.
  • Llegan 10 empleados, o sea, n = 10.

La probabilidad de que el guardia de seguridad encuentre al menos uno en la base militar restringida es dada por:

P(X \geq 1) = 1 - P(X = 0)

En que:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

Por eso:

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1074 = 0.8926

Hay una probabilidad de 0.8926 = 89.26% de que el guardia de seguridad encuentre al menos uno en la base militar restringida.

Puede-se aprender más a cerca de la distribución binomial en brainly.com/question/25132113

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\huge{ \boxed{ \sf{ \frac{4}{3} }}}

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