Answered

Find the best solutions to your problems with the help of IDNLearn.com. Get thorough and trustworthy answers to your queries from our extensive network of knowledgeable professionals.

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.

Sagot :

GinnyAnsweridn

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)

Learn more about Binomial distribution here:

https://brainly.com/question/33656163


We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.