4

QUESTION 13A system Is made of four independent components connected &5 shawn In the fgure below: The probabillties that components A B, € and D work prop...

Question

QUESTION 13A system Is made of four independent components connected &5 shawn In the fgure below: The probabillties that components A B, € and D work properly are 0.95,0.93,0,78 and 0.85 respectively-Find the probability that the system works propely: Give your answer to 3 decimal palces:

QUESTION 13 A system Is made of four independent components connected &5 shawn In the fgure below: The probabillties that components A B, € and D work properly are 0.95,0.93,0,78 and 0.85 respectively- Find the probability that the system works propely: Give your answer to 3 decimal palces:



Answers

Consider a system of components in which there are 4 independent components, each of which possesses an operational probability of $0.9 .$ The system does have a redundancy built in such that it does not fail if 3 out of the 4 components are operational. What is the probability that the total system is operational?

So in the code below, we have that seven round of numbers are generated and they're all indexed one by one into the vector U. So you is indexed. It's Ah, uh, vector of random numbers, which has seven rows and one column. And so we have one for each of the seven components. Now, the sequence of end or conjunctions, as we have and or here this match is a serious and parallel ties and the system designed. So once you're run this matter at court, you're gonna get a is equal to 8159 So probably of a hat should take the back answer. That should be probably probably Hat of A is equal to 8159 over 10,000 which is equal to 0.81 flight.

Well, it's probably have been given a circuit and we would like to find the probability that the circuit works. No, no, the for its work we need A and B to work or we need to C D and E door because we have an overlap here. We also need to subtract off the probability then it maybe works. And C d E works. The probability of a be working, he has a probability of 0.7 B has a probability of also 0.7. Mhm. And so when we take 0.7 times 0.7, this is going to give us 0.49 The probability of C D. E. Working. The probability of C working this 0.8. Yeah. The probability of the working this 0.8, probability of E working is pointed. So when you multiply 0.8 by itself three times as 30.512 Now the probability of a B and C D E. Working because these are independent is the probability of a B times the probability of C D. E. Yeah then whenever we multiply those together this gives us 0.25 oh 88 So now we put these on line up top so we take 0.49 plus 0.512 minus 0.25 oh 88 Right? This gives us our total probability of 0.75112 Yeah. Now in me we want to find the probability yeah that it works given that it works. What's the probability that A is not working? So the probability A does not work. So I saw a compliment given that the whole system works well. This is equal to the probability that A doesn't work and the whole thing does work over the probability that it works. Mhm. Mhm. And now the probability that works, we just found out from that last part this 0.75112 Now, for the probability that it works and it doesn't work, there's a 0.3 chance today works and then a 0.51 to chance. But the other part works. And so this means there's a point 1536 and then that part came from 0.3 for a not working and 0.8 to the third for the other parts working. So if we take this fashion 0.153 6/7 5112 this gives us our probability of 0.20 four or five.

In this question, we're talking about K out of end systems and that each of the end components in each system have a probability of working of 0.96 so we could define that as a success for a given component. If it works, that is a success, and we can consider a K out of N system as looking at end. Samples in each of these n trials can either have a success or a failure. So basically a K out of an system can be viewed. As with a number of successes can be viewed as the number of components in the kit of end. That air working can be viewed as binomial random variable were there en trials and their probability of success is 0.96 So for part A were given a three component system and arrest. What is the probability that exactly two components function? So here we can say the number of components functioning is the binomial random variable based on three trials and a probability of success of 0.96 and we want the probability that exactly two of the components successful successfully function, which comes out to a probability of approximately zero point 111 now for B were asked, What is the probability that at two other three system works, two out of three system means that we must have at least two components working? So what is the probability that the number of successes is at least two? It's gonna be written as one minus probability of, at most one success, which comes out to about zero point 995 now. CS. What is the probability of a three out of five system working? So if the number of successes here, a number of successful components is a binomial random variable based on five trials and the probability of success of 0.96 so we need at least three of the components to work. So what is the probability that X is at least three? It's equal to one, minus the probability that X is, at most two. And this probability probability of this system working is approximately 0.999 four he is. What is the probability of a four out of five system working so again we're using this seem random variable at this time We need at least four successes, which comes out to about 0.985 and finally for party were asked, What does the component probability need to be so that four out of five system will function with probability at least 0.9999? So we're talking about a number of successes is a binomial random variable and there's five trials. It's, ah, five component system, and we'll give it probability successes p. So we're trying to solve for P. And we want the probability that it works, which is the probability that, at least or components function to be greater than or equal to 0.9999 We could also write this the probability that exactly four components, plus the probability that exactly five components work is greater than or equal to zero point 9999 Now, if we use the equation for the probability mass function for a binomial random variable, we can make this equation look like this. So it's so the first term is five. Choose for times P to the exponents four times one minus p to the experiment one plus five choose five times, pleaded exponents five. And this comes out to minus four times p to export and five plus five times P. Diddy Explode and four. And if we subtract 0.9999 from both sides and really what we could do? Here's to find the minimum value for P. We can just equate this to zero, and so we have to solve four P in this equation. So I used software to sell for this and give me P is equal to about 0.9969 So in order for a four out of five system toe work, with probability at least 0.9999 we need P to be at least that reliable. So we need P to be greater than or equal to zero point 9969 where p is the component reliability.


Similar Solved Questions

5 answers
7. Extra Credit: A clock has a minutc hand of 'length 4 cm and a hour hand of length 3 cm. Find the rate of change of the distance belween the tips of the hand at 7.50 pm:
7. Extra Credit: A clock has a minutc hand of 'length 4 cm and a hour hand of length 3 cm. Find the rate of change of the distance belween the tips of the hand at 7.50 pm:...
5 answers
322 29. (6.4) Evaluate dx using the formula Vz6 16du=lnlu + Vu? Vu _ a a2|+C_
322 29. (6.4) Evaluate dx using the formula Vz6 16 du =lnlu + Vu? Vu _ a a2|+C_...
5 answers
1A bar magnetic north points in the same direction as a compass north when exposed to a magnetic field? (True or False):q Earth is a giant magnet is the north pole of Earth's giant magnet a magnetic north pole?Which way does the field point in the magnetic shown draw arrows onto field lines to show the direction?
1 A bar magnetic north points in the same direction as a compass north when exposed to a magnetic field? (True or False): q Earth is a giant magnet is the north pole of Earth's giant magnet a magnetic north pole? Which way does the field point in the magnetic shown draw arrows onto field lines ...
5 answers
The radius of convergence for the power series Z Wx_32 Is n = 5"nSelect one: a.5b_C. V5d. V6
the radius of convergence for the power series Z Wx_32 Is n = 5"n Select one: a.5 b_ C. V5 d. V6...
5 answers
Let XIn] be a WSS process with autocorrelationRx[m] = o3alml + o%o[m], Ia] < 1Show that X[n] is an ARMA(p,q) process and find the values of p and qAssume nOW that 03 models for X[n]o3 = 5 and0.6. Find the parameters of the following linearAR(1). MA(1) ARMA(1,1)
Let XIn] be a WSS process with autocorrelation Rx[m] = o3alml + o%o[m], Ia] < 1 Show that X[n] is an ARMA(p,q) process and find the values of p and q Assume nOW that 03 models for X[n] o3 = 5 and 0.6. Find the parameters of the following linear AR(1). MA(1) ARMA(1,1)...
5 answers
OeankioActudguNyaton LudCcoima Ibody wrh enrtulutencud Insurolodinga *In 'utrouciutgltluenlannncn a bodremotuture Tlalter {Memal M-TolAGim eaete FumunuleteMnimtuen Iss nacaginn nensEne ua iutu Orf ArutmruxuscumnoruivuGnta'p MNeton Ccdna[atuaeanmbuTuttelueaalleTuctmulte(Round to tho ncnrast Ircager )
Oeankio Actudgu Nyaton Lud Ccoima Ibody wrh enrtulute ncud Insurolodinga *In 'utrouciutg ltluenlannncn a bodr emotuture Tlalter { Memal M -Tol AGim eaete Fumunulete Mnimtuen Iss nacaginn nens Ene ua iutu Orf Arut mruxus cumnoruivu Gnta'p MNeton Ccdna [atuaeanmbu Tutteluea alle Tuctmulte...
5 answers
NOMQ11 1 PointMcq~1 0 -3ficss JestSuppose Band that C is a 4 X 4 matrix with det(C) = ~4. If it ispossible, evaluate det(C-1B).Fm36~cnno144 Cannot be determined from the given information
NOM Q11 1 Point Mcq ~1 0 -3 ficss Jest Suppose B and that C is a 4 X 4 matrix with det(C) = ~4. If it is possible, evaluate det(C-1B). Fm 36 ~cnno 144 Cannot be determined from the given information...
5 answers
Eered o2 curve ( y = Jx(/-xt 0+x44
Eered o2 curve ( y = Jx(/-xt 0+x44...
5 answers
Find the mass and center of mass of the solid E with the given density function Elies under the plane 2 = 2 + x + and above the region in the xY-plane bounded by the curves Y = Vxiy = 0, and * = 1; P(x, Y, 2) = 9.(x,y,z)
Find the mass and center of mass of the solid E with the given density function Elies under the plane 2 = 2 + x + and above the region in the xY-plane bounded by the curves Y = Vxiy = 0, and * = 1; P(x, Y, 2) = 9. (x,y,z)...
5 answers
Problem 8 points) . It takes 25 mL of 0.24 M Fe?*(q) to titrate 25 mL of KzCrzO_(aq) in the reaction: Cr,o? 6Fe?+ 14Ht 2Cr3+ 6Fej+ 7Hz What is the molar concentration of KzCrzO, Enter your answer in the box provided with correct units and sig figs The molar concentration Answer: of KzCr2Oz is [Kzcrzow]
Problem 8 points) . It takes 25 mL of 0.24 M Fe?*(q) to titrate 25 mL of KzCrzO_(aq) in the reaction: Cr,o? 6Fe?+ 14Ht 2Cr3+ 6Fej+ 7Hz What is the molar concentration of KzCrzO, Enter your answer in the box provided with correct units and sig figs The molar concentration Answer: of KzCr2Oz is [Kzcrz...
5 answers
State the area 0f the region; determined by the lines; y = 6r v = 3 + 2, V = 61 11, y = 37 | 5 with proper uv-transformation y = 61 . v = 31 + 2, V = 62 11, y = 3r + 6 dogrulari Ile sinirl bolgenin alanini uygun uv-dondsumu ile Ifade ediniz), integrand function (integrant fonksiyonu) the limits ofu (u nun sinirlan) the Iimits of v (v nin Sinirlan)
State the area 0f the region; determined by the lines; y = 6r v = 3 + 2, V = 61 11, y = 37 | 5 with proper uv-transformation y = 61 . v = 31 + 2, V = 62 11, y = 3r + 6 dogrulari Ile sinirl bolgenin alanini uygun uv-dondsumu ile Ifade ediniz), integrand function (integrant fonksiyonu) the limits ofu ...
5 answers
If a carousel is rotating at 2.5 revolutions per minute, explain how to find the linear speed of a child seated on one of the animals.
If a carousel is rotating at 2.5 revolutions per minute, explain how to find the linear speed of a child seated on one of the animals....
5 answers
Suppose a 500.mL flask is filled with 0.40mol of H2 and 0.80mol of HCl. The following reaction becomes possible:+H2gCl2g 2HClgThe equilibrium constant K for this reaction is 0.465 at the temperature of the flask.Calculate the equilibrium molarity of Cl2. Round your answer to two decimal places.
Suppose a 500.mL flask is filled with 0.40mol of H2 and 0.80mol of HCl. The following reaction becomes possible:+H2gCl2g 2HClgThe equilibrium constant K for this reaction is 0.465 at the temperature of the flask.Calculate the equilibrium molarity of Cl2. Round your answer to two decimal places....
5 answers
Let F tuicate Ilow lines. =xity+k Find the general cquation of a flow line. (b) Find the flow line through the point (1,1,2).
Let F tuicate Ilow lines. =xity+k Find the general cquation of a flow line. (b) Find the flow line through the point (1,1,2)....
5 answers
0 5 3 Sab? €54226 6426€
0 5 3 Sab? € 54226 6426 €...
5 answers
(ast yeat, Ahmad tiud 530,000 to invest H Mvcsted cmu ucount tFuk pild 690 srrple_Interest pct YCal ahu he Kwvestcd tfle: (E4 puid 790 sutpole mlerest per yeal Nltct onc yedr he treivcd 0 tolal 0( $z010 Irtoc Muw uuic cuetct nvcs hcCuUrit ?Hccmlt tatTrx uCcount;Second account:
(ast yeat, Ahmad tiud 530,000 to invest H Mvcsted cmu ucount tFuk pild 690 srrple_Interest pct YCal ahu he Kwvestcd tfle: (E4 puid 790 sutpole mlerest per yeal Nltct onc yedr he treivcd 0 tolal 0( $z010 Irtoc Muw uuic cuetct nvcs hcCuUrit ? Hccmlt tat Trx uCcount; Second account:...
5 answers
Mass of 60.0 g moves horizontally on a frictionless surface It is connected to a wall by a spring_ It oscillates with a Period of 0.0590 sWhat is the Force Constant of the spring?m
mass of 60.0 g moves horizontally on a frictionless surface It is connected to a wall by a spring_ It oscillates with a Period of 0.0590 s What is the Force Constant of the spring? m...

-- 0.020827--