5

3. (S 2.1) A system contains two components; and B_ The system will function only if both components fuuction: The probability that functions is 0.98 the probabilit...

Question

3. (S 2.1) A system contains two components; and B_ The system will function only if both components fuuction: The probability that functions is 0.98 the probability that B fune- tion is 0.95 and the probability that or B function is 0.99 Wat is the probability that the system fuuctions?(5 22) Iu certain state. licens plates consist of thrce letters followel by three mtubers() How HAHI (lillereut liceust plates Gu Ix uudke" How ManY dlillerut liccnst plates can Ix Hudle iu which Hlo katter

3. (S 2.1) A system contains two components; and B_ The system will function only if both components fuuction: The probability that functions is 0.98 the probability that B fune- tion is 0.95 and the probability that or B function is 0.99 Wat is the probability that the system fuuctions? (5 22) Iu certain state. licens plates consist of thrce letters followel by three mtubers () How HAHI (lillereut liceust plates Gu Ix uudke" How ManY dlillerut liccnst plates can Ix Hudle iu which Hlo katter or Mller "ppcIrS MOTU thahl Once! license plate is chosen at rallom: What is the probability that no letter or WHher appear more than once?



Answers

A $k$ -out-of-n system functions provided that at least $k$ of the $n$ components function. Consider independently operating components, each of which functions (for the needed duration) with probability $96 .$
(a) In a 3-component system, what is the probability that exactly two components function?
(b) What is the probability a 2 -out-of-3 system works?
(c) What is the probability a 3 -out-of-s-s system works?
(d) What is the probability a 4 -out-of-5 system works?
(e) What does the component probability (previously 96$)$ need to equal so that the 4 -out-of-s system will function with probability at least. 9999$?$

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.

So for this question, let a B the event that the first component functions and be be the event of the second component functions. So probably a B is equal to 0.9 and probably of a union. Be where either one functions is 10.96 and probably a intersect Be this 0.75 So if we use additional rule or the principle of inclusion exclusion, then we have probably a union B plus property of being sorry product of a union B is equal to probably eight. Plus probably will be Linus Apology a intersects B, which implies that 0.96 is equal to probably of a plus 0.9 minus 0.75 So the probability of a his 0.81 So the property of be given a is equal to property of be intersect a divided by probably of a, which is 0.75 divided by 0.81 which is 0.9 to 6, repeating or approximately 0.92 so

For this problem. We use the fundamental counting principle, and we multiply the number of options for the first letter or number by the number of options for the 2nd 1 and so on and so forth. So for part A and part B, we're going to be multiplying six numbers together for part A. The license plate has three letters, followed by three digits. So for letters, we have 26 choices for the first letter, 26 choices for the second letter and 26 choices for the third letter and then for digits. We have 10 choices for each, so we have 10 times, 10 times 10. And when we multiply all of those together we end up with 17,576,000 different license plates in Part B. They switched it around, and they put the digits first and the letters after. So it's just going to look like this 10 choices for each digit and then 26 choices for each letter. So we're multiplying the same numbers together, so we end up with the same number of choices. 17,576,000 and then finally, for part C they're going to insert an extra letter before the letters and the digits. So there's 26 choices for the letter, and then we have our previous answer, so we could take our previous 17 million something and multiply it by 26 we end up with 456 million 976,000 license plates.

Okay for this problem we're going to be looking at on all the different ways you can make a license plate is a very tip ability problem. So we're gonna look at first is that we've got right now what we know here. We know that, um, for automobile license plates, we can have different letters followed by different numbers. What I do with my students is I get one example some here's an example. This kind of gets depart, see what they say. Well, letter A. We talk about letters being done, so maybe you'll have X y Z and your license plate, and then maybe we'll have three different number. Possibility is X Y Z and 123 That's an example, right? So part A says, How many different ways are there to have ah, three letter combination? It's really three letter arrangement because the order is the order matters in this case. So X y Z is different than xz. Why? So that affects the math a little bit. So we do all the different possibilities. So let's look apart. A So, um and it does say the state does not use valve or the letter y so Oh, shoot. I mean, stick there. So I'm just gonna just for reference you We couldn't have X y Z because they say no vowels and no letter. Why? So let's see wells and know why is the reason being that out? Because that affects our number possibility. There's 26 letters in the alphabet, so they're gonna basically knock out the five vowels in the letter y So we could say I can't use that. So maybe we'll be X daisy. That's what that means there. So what that means is that we have 20 letters combinations, 20 to pick from. So for part, A says how many different each letter can only appear once on any given license plate. How many different sets of three letters or possible? So if you only do it once Well, for your first pick, you have 20 different pics. And for your second pick, you can't use that. Whatever you pick again, let's say you pick an extra can't pick use X again. That drops you down to 19 picks. And for the third combination, that's 18 letters to choose from, so people play all three of those together that means that you have 6840 different arrangements. So that's party. Let's look apart being they say, Well, how many different ways of the new numbers. So, for part B, we know that we have 10 digits were picking three. There were zero accounts of a digit. All right, so for digits have been different. Three letter digits. Can we have three letter combinations I should needs were combination that usual letter word arrangements cause border matters and not repeating matters. That's why the numbers go down. So that's three number speed digits. So my example there, 123 could be some 1012 could be another one. But in general, we know that we have 10 different digits that we could pick. And then ah, I called the domino effect. So you have 10 you pick a certain number and then you're a number of different numbers to pick from was down by one and the 3rd 1 goes down by another one. So you do 10 times nine times eight. So if you 10 times nine times eight, that gives you 720 different arrangements of three digits, so That's the answer for part B. Important sees where you put it all together. So part C. Wherever sand. Okay, we're gonna put all the letters together, so we think of all the different license plates. And the whole purpose of that is we have different license plates with three letters and three numbers. So we're looking for the number of about license plates. Their possible unique license plates, like your parents have a license plate that's different than the neighbors license plates were really doing here is taking these together. So really, them? I'm not going to read you the math, but we've done it for parts A and B. So you take 2010 19 times 18 times, 10 times, nine times eight. Because we've already partially done the numbers, we just have to multiply those two together. So what we have to do This just takes 6840 combinations of the letters Time. 720 digit combinations. Overall, our final final answer. Millions of your state has all these possibilities for everybody to have a unique license plates. So four million and 24,000 800 different license plates. That's a nice story, a little problem. So that's how they do it. All right, so you get the arrangements. Big thing. Where there was watched what I call a domino effect. It goes down each time. He's not repeating letters, and we had 26 letters in the alphabet, but no vowels in a way.


Similar Solved Questions

5 answers
Estimate the area under the graph of the given function on the stated interval as instructeflx) =x? between X = 1 and X = 5 using a left sum with four rectangles of equal width
Estimate the area under the graph of the given function on the stated interval as instructe flx) =x? between X = 1 and X = 5 using a left sum with four rectangles of equal width...
5 answers
Use the accompanying Credit Risk Data to perform the activities in parts & thrc Click the icon to view the Credit Risk Data Iype an integer Or decimal rounded [0 IWO decimal places as needed Combined Checking % Cumulative % Cumulative % and Savings Customers] 12,653 7,084 5,747 3,432 2,935/ 1,422 1,402 1,248Enter your answer in the edit fields and then click Check Answer:
Use the accompanying Credit Risk Data to perform the activities in parts & thrc Click the icon to view the Credit Risk Data Iype an integer Or decimal rounded [0 IWO decimal places as needed Combined Checking % Cumulative % Cumulative % and Savings Customers] 12,653 7,084 5,747 3,432 2,935/ 1,42...
5 answers
During : certain week the number of daytime and nighttime emergency calls to parandics in Twge city IS given the table Using = 0,05 level of significance , determine mrnw"dies receive mre calls night, Whal is the p-value? (You will have [0 find the pdf )Day Night
During : certain week the number of daytime and nighttime emergency calls to parandics in Twge city IS given the table Using = 0,05 level of significance , determine mrnw"dies receive mre calls night, Whal is the p-value? (You will have [0 find the pdf ) Day Night...
5 answers
Roaann Contrti Penpdc TbeCoraldeln crem col Lmtcint c6)+Eo(9) ~ CO (g) Hite)Par AHjeCitEnn dhtonn 0i Enlmnad Dnaero d 1 0 alm Mdoneolen0J1dx nrntn LLnqIerd LonToncentn
Roaann Contrti Penpdc Tbe Coraldeln crem col Lmtcint c6)+Eo(9) ~ CO (g) Hite) Par A HjeCitEnn dhtonn 0i Enlmnad Dnaero d 1 0 alm Mdoneolen0J1dx nrntn LLnqIerd Lon Toncentn...
5 answers
Module 2 Problem 1 a) Let T R2 7 R2 be a linear transformation. Three vectors V1, Vz, W in R2 and the vectors T(V1) , T(V2) are shown below . Sketch T(w). Explain.T( )T62)-2 b) If A = and AB = 1-2 5 |determine the first and second columns of B_6 ~9
Module 2 Problem 1 a) Let T R2 7 R2 be a linear transformation. Three vectors V1, Vz, W in R2 and the vectors T(V1) , T(V2) are shown below . Sketch T(w). Explain. T( ) T62) -2 b) If A = and AB = 1-2 5 | determine the first and second columns of B_ 6 ~9...
5 answers
Acovalent bond is Iikely to be polar under which of the following conditions?the two atoms sharing electrons are of the same elements carbon Is one ol Ihe (wo atoms sharing electrons the two atoms sharing electrons are equally electronegative one of the atoms sharing electrons is more electronegative than the other atom
Acovalent bond is Iikely to be polar under which of the following conditions? the two atoms sharing electrons are of the same elements carbon Is one ol Ihe (wo atoms sharing electrons the two atoms sharing electrons are equally electronegative one of the atoms sharing electrons is more electronegati...
5 answers
In the animal kingdom; the sex that is more selective in choosing a mate isconsistently females_b: consistently maleswhichever sex is most brightly colored or has the most elaborate song:whichever sex does the most parental care_e. whichever sex does the least parental care_
In the animal kingdom; the sex that is more selective in choosing a mate is consistently females_ b: consistently males whichever sex is most brightly colored or has the most elaborate song: whichever sex does the most parental care_ e. whichever sex does the least parental care_...
5 answers
Nual2345 answcred this '239 answersWas this answer helpful?45 2Slack -AityPueUeceeculgTiut"CrtcD>[ >Project Ouration; 12 Weeks Crtical activities: DEEH
Nual2345 answcred this '239 answers Was this answer helpful? 45 2 Slack - Aity PueUeceeculg Tiut" Crtc D>[ > Project Ouration; 12 Weeks Crtical activities: DE EH...
5 answers
In this question, you will solve an integral problem using the method of substitution: (a) Make the substitution U = 5 +2 and write the integrand as a function of U_6x dx 5+22du(D) Hence solve the integral as a function of &, and a constant of integration upper-case Cc) Now write the integral as a function of the original variable, (and C)
In this question, you will solve an integral problem using the method of substitution: (a) Make the substitution U = 5 +2 and write the integrand as a function of U_ 6x dx 5+22 du (D) Hence solve the integral as a function of &, and a constant of integration upper-case C c) Now write the integra...
5 answers
Use an addition or subtraction formula to find the solutions of the equation sin(T) cos(- Zr) ~sin( = 2-)cos(rr) + ! that are in the interval [0. 10) .
Use an addition or subtraction formula to find the solutions of the equation sin(T) cos(- Zr) ~sin( = 2-)cos(rr) + ! that are in the interval [0. 10) ....
5 answers
Use the Ideal Gas Law to explain how your body controls the inhaling of air into your lungs
Use the Ideal Gas Law to explain how your body controls the inhaling of air into your lungs...
1 answers
Internet Retail Sales. Online retail sales totaled $\$ 133.6$ billion in $2008 .$ This was about three times the total in 2002 . (Source: U.S. Census Bureau) Find the online sales total in 2002 .
Internet Retail Sales. Online retail sales totaled $\$ 133.6$ billion in $2008 .$ This was about three times the total in 2002 . (Source: U.S. Census Bureau) Find the online sales total in 2002 ....
3 answers
6 . Define the set of functionsA = f (-1,1) = Rlf(c) = anzn for x in (_1,1) and lanl n=0 n=0(a) Show that A is a normed linear space with the norm Ifli = Enz-o lanl: b) Define the antidifferentiation map on A byUn A(f)(c) = zn+1 n + 17 n=0Show that A is bounded operator_ Describe the range of this operator: c) Is the transformation A : A 57 ranA invertible? If S0, is the inverse transforma- tion also bounded operator?
6 . Define the set of functions A = f (-1,1) = Rlf(c) = anzn for x in (_1,1) and lanl n=0 n=0 (a) Show that A is a normed linear space with the norm Ifli = Enz-o lanl: b) Define the antidifferentiation map on A by Un A(f)(c) = zn+1 n + 17 n=0 Show that A is bounded operator_ Describe the range of th...
5 answers
Hol 1 B= V2 0 d. 2ndHol B= V2 ud0 e:1 B= Hol 0 f V2 nd0 gHol B= V2 nd0 h.B = Kol 2ta Vz
Hol 1 B= V2 0 d. 2nd Hol B= V2 ud 0 e: 1 B= Hol 0 f V2 nd 0 g Hol B= V2 nd 0 h. B = Kol 2ta Vz...
5 answers
9) A clinical laboratory scientist performs 30 replicate hemoglobin determinations on a single blood sample. When statistics are used to determine the precision of the method, the mean is 13.8 g/dl and 1 SD is 0.1 g/dL. This means that 95.5% of the results on this specimen lie:A) between 13.6 and 14.0 g/dL: B) between 13.7 and 13.9 g/dL C) between 13.4 and 14.2 g/dL: D) between 13.5 and 14.1 B/dl: Show your work:
9) A clinical laboratory scientist performs 30 replicate hemoglobin determinations on a single blood sample. When statistics are used to determine the precision of the method, the mean is 13.8 g/dl and 1 SD is 0.1 g/dL. This means that 95.5% of the results on this specimen lie: A) between 13.6 and 1...

-- 0.020911--