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III) DISTRIBUCIÓN BINOMIAL

1. La probabilidad de que una cierta clase de componente pase con éxito una determinada prueba de impacto es [tex]\(\frac{3}{4}\)[/tex]. Si se toman al azar 10 componentes, encuentre la probabilidad de:

a) Que exactamente 2 de los 10 componentes que se prueban pasen la prueba.

b) Que dos o menos componentes salgan defectuosos.



Answer :

GinnyAnswer

Final answer:

The binomial distribution is utilized to determine the probability of a specified number of successes in a fixed number of trials with a constant probability of success. The detailed answer explains how to calculate the probabilities of exact successes and a range of failures in the given scenario.


Explanation:

Binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

  1. For the given situation, with a probability of success (p) of 3/4:
  2. a) To find the probability of exactly 2 successes out of 10 trials, you can use the binomial probability formula:
    P(X=2) = (10 choose 2) (3/4)^2 (1/4)^8
  3. b) To calculate the probability of two or fewer failures (defective components), you need to find the cumulative probability of having 0, 1, or 2 failures:
    P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

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