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2) Your design team is working on a rocket that requires four ignition systems to operate. Each ignition system is a one-use device (try to ignite once cannot try a...

Question

2) Your design team is working on a rocket that requires four ignition systems to operate. Each ignition system is a one-use device (try to ignite once cannot try again) The reliability, ie. likelihood of working; for a ignition system is 0.85.What is the probability of successfully operating the rocket if your team purchases 6 ignition systems?

2) Your design team is working on a rocket that requires four ignition systems to operate. Each ignition system is a one-use device (try to ignite once cannot try again) The reliability, ie. likelihood of working; for a ignition system is 0.85.What is the probability of successfully operating the rocket if your team purchases 6 ignition systems?



Answers

A starter motor used in a space vehicle has a high rate of reliability and was reputed to start on any given occasion with probability. $99999 .$ What is the probability of at least one failure in the next 10,000 starts?

In the current situation Off quality control. There is a spacecraft which has toe, um, and okay, systems. So one of them is the main system on the other Minister. That's no no ability. While the spacecraft is at work duration of the flight. Is that the having the flight in decoration? The probability off both. Would, they say, originated M. And we do not be so in and be okay. There, there. So at least one off them functioning. Okay, that is equal to 0.9 55 So then what? What is the probability that both are failing before I straight out, give you the answer? Okay. I can just right, like one minus the 10.9855 or something. We need to understand why. What? Whatever. So this is basically a classic case off normal coin toss. Head head could fail still ahead on tells you think off head as the success, Andi, till as the failure. So there are instead of two coins we have two spacecrafts on. That's why if both the spacecrafts are working fine, we can say success, success or first when the main one working fine, but the other one is failing to success. It's an failure on. Then we can have the main one mean system feeling. With the backup system working satisfactorily. Is this on? Then the last case would be this. Now think off at least one off them. Working fine means probability of this plus probability of this plus probability of this. What is this? Total property. This is your 0.9855 and we always know that the total probability should be one. So that's why What is the probability off this part? Remaining part, obviously. One minus the rest off it on. Hence we get one minus zero point 9855 Toby the answer which will be five on, then four and then one. Siegel. So 0.145 is the answer. Let us check it again. So by plus five seed or and then see you again and then sleepwalking. Mhm. Sit on women one. Oops, funny whatever it is. But this is how we can verify. I'm again. I'm telling that calculation is not what we are focusing primarily focusing because thes are very key concepts of property and we should be 100% comfortable around the concept. Off probability off. A less probability off a compliment is one. If you see, at least one of them working is a complementary function or set off none of them working. Both are failing. So more than anything, the main primary objective of this exercise is to make you understand that how these two even zehr related with each other. All right, I hope I could explain it. Well, let me know if you have

This problem is about components on a ship and whether they fail. So let's let Andy the event that the main system has a failure. Let's let Bebe the event that the backup system has a failure and so were given that the probability that they both fail is 0.148 and we're also given we can assume the chance that that they're equally likely to fail separately. And now to solve this problem. There's one other unstated assumption that really should be made a little bit more. Keep clear in the problem statement. So with the information we were given, it's not necessarily enough now, too. Find the probability that the main system fails because it could be that there is some dependence between these two. I believe that the problem is really implying that they're independent events. So I mean, if this is really a backup system, it should be ableto work, no matter what's happened to the main system. So whether the main has failed or not, the backup should have the same chance of working. So I think it is safe for us to assume that M and N M and be are independent events, meaning that the conditional probabilities of say and given that be happens is still equal to the probability of em. And an important property of independent events is that probability of their intersection is equal to the product of their probabilities, which in this case, is P. Of M squared. We owe that p of B equals P of em that tells us that P of them is equal to the square root of 0.148 which is roughly 12%.

Yeah that's probably we're told From a lot of 10 missiles. Three are selected at random. In fact. Now the lot contains four defective missiles as we have four defective. And so it's non effect mm. You know, hey we want to find the probability that the three that we choose are all working. Now. Those are six out of 10 chances. The first one we choose works since we've already chosen one of the ones that work. So probably the next one works is five out of nine. We have one less total and we have one less working. And then lastly the probably the last one works is four out of eight. For the same reason we have one less total and one less working. Okay. Multiply all these together will give us 16 and so there's a 16 chance that all of them work now on me. We want to find the probability that at most two will not fire. So the probability that the number of do not work Is less than or equal to two. This is equal to 1-. The probability that D. is equal to three. You'll notice that the total number we're choosing is equal to three and so there's less than equal to complement. That would be a 23 Which is 1-. And then we have four defective So they're probably the first is the effective is 4/10 Probability. The second is the fact was three nights And then to eight. So to get our probability we're going to multiply these together. Are we evaluate this. Mhm. Mhm. This gives us 29 out of 30.

This problem, we want to find the probability that the system failed and the system only fails of all the components failed. No. What? This means the probability mhm, that the system does not fail As usual. 1- the probability that it does fail. Probably it does feel means that all of the components have to fail. No one operates with a .95% probability fails. .05, probability two is with .80, so it fails. 0.20 Three fails at a rate of .9 0.10. Then four works at a 97% chance. That's what fails at point on three. And so now we just need to evaluate this on a calculator And when we do this gives us 0.99997. That's the probability it does not feel.


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