1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DanielleElmas [232]
2 years ago
6

A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identi

cal components, each with a probability of .2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components operate independently. Find the probability that a exactly two of the four components last longer than 1000 hours. b the subsystem operates longer than 1000 hours.
Mathematics
1 answer:
Tcecarenko [31]2 years ago
4 0

Answer:

a. 0.1536

b. 0.9728

Step-by-step explanation:

The probability that a component fails, P(Y) = 0.2

The number of components in the system = 4

The number of components required for the subsystem to operate = 2

a. By binomial theorem, we have;

The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) is given as follows;

P(Y = 2) = \dbinom{4}{2} × 0.2² × 0.8² = 0.1536

The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) = 0.1536

b. The probability that the system last longer than 1,000 hours, P(O) = The probability that no component fails + The probability that only one component fails + The probability that two component fails leaving two working

Therefore, we have;

P(O) = P(Y = 0) + P(Y = 1) + P(Y = 2)

P(Y = 0) = \dbinom{4}{0} × 0.2⁰ × 0.8⁴ = 0.4096

P(Y = 1) = \dbinom{4}{1} × 0.2¹ × 0.8³ = 0.4096

P(Y = 2) = \dbinom{4}{2} × 0.2² × 0.8² = 0.1536

∴ P(O) = 0.4096 + 0.4096 + 0.1536 = 0.9728

The probability that the subsystem operates longer than 1,000 hours = 0.9728

You might be interested in
The formula for the volume of a cube is V = s³, where s represents the side length of the cube. If a cube has a side length of 4
Alla [95]

Answer:

91.125 or 729/8

Step-by-step explanation:

take 4.5^3 to get 91.125

7 0
3 years ago
Read 2 more answers
Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
Nimfa-mama [501]

The solution of the equation are as follows:

x = 6 and y = -5

<h3 />

<h3>How to solve the system of equation?</h3>

4x + 5y = -1

-5x - 8y = 10

Therefore,

20x + 25y = -5

-20x - 32y = 40

-7y = 35

y = -5

Hence,

4x + 5(-5) = -1

4x - 25 = -1

4x = -1 + 25

4x = 24

x = 24 / 4

x = 6

learn more on equation here:brainly.com/question/14383993

#SPJ1

6 0
1 year ago
Can someone do the one thats cirlced ty :D
vichka [17]

Answer:

5/3 or 10/12

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What’s the square root of 48/81?
chubhunter [2.5K]
4 square root of 3 over 9
7 0
3 years ago
Read 2 more answers
A bank loaned out $21,500 , part of it at the rate of 11% annual interest, and the rest at 10% annual interest. The total intere
Luda [366]

Answer:

The loaned amount at 11 % is $ 19,000

The loaned amount at 10 % is $ 2,500

Step-by-step explanation:

Given as :

The total loan amount = $21,500

The total interest earn = $2,340.00

The rate of interest are 11 %  and 10 %

Let The loan amount at 11 % rate = $P

and The loan amount at 10 % rate = $21,500 - $P

Let The loan took for 1 year

Now,<u> From Simple Interest method </u>

Simple Interest = \dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}

SI_1 = \dfrac{P_1\times R_1\times \textrm Time}{100}

Or, SI_1 = \dfrac{P\times 11\times \textrm 1}{100}

Similarly

SI_2 = \dfrac{21,500 - P\times 10\times \textrm 1}{100}

∵  SI_1 +  SI_2 =  $2,340

Or, \dfrac{P\times 11\times \textrm 1}{100} + \dfrac{21,500 - P\times 10\times \textrm 1}{100} = $2,340

Or, 11 P - 10 P + 215000 = 234000

Or, P = 234000 - 215000

∴ P = $ 19,000

And $21,500 - $ 19,000 = $ 2,500

Hence The loaned amount at 11 % is $ 19,000

And     The loaned amount at 10 % is $ 2,500    Answer

8 0
3 years ago
Other questions:
  • 4 times a number increased by 2 is the same as 10 more than 2 times the
    6·1 answer
  • Please Help With Math... Brainliest
    9·1 answer
  • Solve for j. please help meee
    11·2 answers
  • Percent means per____"
    5·2 answers
  • Please help me with this, aaaaaa
    13·1 answer
  • This question is confusing. Please help me!This question is confusing. Please help me!
    9·2 answers
  • Find the sum of -3/4+ -7/6
    8·1 answer
  • Are My answers Correct? I NEED ANSWERS!
    11·1 answer
  • Y=-3x + 1
    5·1 answer
  • What are two variables that might be positively related to academic success?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!