El diseño de un sistema requiere instalación de 2 componentes iguales. El sistema completo funcionará si al menos 1 de los componentes funcionan,mientras que un sistema alternativo requiere cuatro de sus componentes funcionará si al menos 2 de sus componentes están funcionando.
La probabilidad de que un componente funcione de manera individual es de 0.9 y cada uno funciona de manera independiente. ¿cuál de los 2 diseños tienen mayor probabilidad de funcionar?

Usando la distribución binomial, se encuentra que el diseño de 4 componentes tiene mayor probabilidad de funcionar.

Para cada componente, solo hay dos resultados posibles. O están funcionando o no estan. La probabilidad de que un compoente estea funcionando es independiente de cualquier otro componente, lo que significa que se utiliza la distribución binomial para resolver esta cuestión.

Distribuición binomial:

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

En este problema:

Diseño de 2 componentes:

La probabilidad de funcionar es [tex]P(X \geq 1)[/tex], que es dada por:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

En que:

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

[tex]P(X = 0) = C_{2,0}.(0.9)^{0}.(0.1)^{2} = 0.01[/tex]

Entonces:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.01 = 0.99[/tex]

Diseño de 4 componentes:

La probabilidad de funcionar es [tex]P(X \geq 2)[/tex], que es dada por:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

En que:

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

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

[tex]P(X = 0) = C_{4,0}.(0.9)^{0}.(0.1)^{4} = 0.0001[/tex]

[tex]P(X = 1) = C_{4,1}.(0.9)^{1}.(0.1)^{3} = 0.0036[/tex]

Entonces:

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0001 + 0.0036 = 0.0037[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0037 = 0.9963[/tex]

[tex]0.9963 > 0.99[/tex], o sea, el diseño de 4 componentes tiene mayor probabilidad de funcionar.

Un problema similar es dado en https://brainly.com/question/25132113

Use place value and properties of operations to find the sum.

5.8
+2.3
= _

Type a whole number or a decimal

Graph the linear function:
r(x)=2

A letter use to represent a number value is called

Whats 4+4+(6x168) and the answer in Spanish

given that x is an acute angle and cos x equals to 2 root 5/5 find without using mathematical tables or a calculator tan (90 - x)​

f(x)=10-9/2x
if f(x)=-53x find x

(WORTH 100 POINTS)On Monday, Latrena sent an email to 5 friends. On Tuesday, each of those friends sent an email to 5 different friends. On Wednesday, each person who received an email on Tuesday sent an email to 5 different friends. How many friends received an email on Wednesday? Enter your answer as a power by filling in the boxes.

Which of the following represents, "The difference between a number and elght Is twenty-two"?
A. N-8=22
B. 8 - N= 22
C. 8 - 22 N

A side of a square is 10 cm longer than the side of an equilateral triangle. The perimeter of the square is 3 times the perimeter of the triangle. Select the equation that represents the scenario when x represents the side of the triangle.

How to simplify the following expressions?
1. 6x-3y+8x-(-4y-3y)
2. 1+8a/4-3+2a

Watch help video
Christian is driving on a long road trip. He currently has 12 gallons of gas in his car.
Each hour that he drives, his car uses up 1.25 gallons of gas. How much gas would be
in the tank after driving for 6 hours? How much gas would be left after t hours?
Gas left after 6 hours:
Gas left after t hours:
Submit Answer
attempt 1 out of 2 / problem 1 out of max 1
Privacy Policy Terms of Service

An election is over and a new student body president has been elected. The new president received 3 votes for every vote received by his opponent. The new president received 2193 votes. How many votes did his opponent receive?

In the fourth grade at Jefferson elementary School, there are 125 students. In the fifth grade, there are 136 students. How many total students are there in fourth and fifth grade?

A bakery must pay the state 8% sales tax on this week's total sales of $2,050. How much sales tax will the bakery pay to the state for this week?

A. $164.00


B. $164.00


C. $256.25


D. $256.25

a service company charges a 5% service fee

-2 as a decimal
Help if you can ik it’s simple I’m just very tired :)

If f(n) = -3n + 10 what is the 5th term???

After 12 years I shall be three times as old as I was 34years ago. Determine my present age

Write an equation for the description.

The length of a rectangle is twice its width. The perimeter of the rectangle is 130 feet.

Use function notation to write the equation of the line
please asap

When Sharon graduates from college, she accepts a job that pays $30,000 for the
first year with a promise of a 10% raise at the beginning of each of the next 9 years.
Samantha graduates the same year and accepts a job which pays $40,000 the first
year with a raise of $1,000 at the beginning of the next 9 years.
а
In which year will Sharon's annual salary first exceed Samantha

Please show step by step. I will chose Brainlyest once it lets me. 5 s and thanks too. Please answer ASAP.

Select all that are equivalent to
Assume a not equal to 0
***please answer fast***

Solve the following expression when
v = 10 and e= 5
2v ÷ e + 3​

1.25(−3.6)
??????????????????????????

njsfkulrnfijrirjir help me help me help me help

Write that down the equation for the lines that is the graphs are depicted below

PLZ HELP 20 points

HELP LAST ATTEMPT !?!!!!!

Frankie charges 30$ per week for tutoring plus a 10$ sign up fee. Complete the table to show the relationship, then graph the table of values. WILL GIVE BRAINLIEST pls no bs answers

The ABC manufacturing firm, the average withdrawal rate for product A is 20
cartons per day, safety stock is 5 days, order lead time is 10 days, and the
order quantity is 45 days.

Requirement: What are the maximum and average quantities of unit loads to be
stored? (Please help me solve this exercise in detail about the requirements of the question)