Redundancy in Computer Hard Drives The Seagate ST8000NM0055 ha...

Question

Redundancy in Computer Hard Drives The Seagate ST8000NM0055 hard drive has a 1.22% rate of failures in a year (based on data from Backblaze, Inc.). For the following, assume that all hard drives are that Seagate model.

a. If all of your computer data are stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? Express the result with six decimal places.

Accepted Answer

Welcome back, everyone. A certain model of solar power inverter has a 2.35% probability of failing within a year. Based on manufacturer testing, assume all inverters used are of this specific model. If an off-grid system uses two identical inverters, each storing backup power, what is the probability that at least 1 inverter functions properly throughout the year? Express your answer rounded to 6 decimal places. A says 0.0. 23,500 B 0.976500 C 0.999448 and D 0.000552. So first of all, let's define an event A. We want at least one inverter to function properly, right? So we're going to say at least One Works Now, for this problem, we're going to use the complement method. So what we want to do is define. An event a bar, which is the opposite event. If at least one works, this means that either one works or two of them work, right? So the opposite event, a bar or the complement of a means that both fail, right? And now, if we're looking for the probability P of A using the properties of probabilities, this is 1 minus the probability of a bar. And this is exactly how we're going to approach this problem. We're going to identify the probability of the complement of A. How do we identify the probability of both of them failing? Well, essentially we know that the probability of one of them failing is 2.35% or 0.0235. So what we're going to do is identify P of a bar by taking 0.0235 and multiplying it by 0.0235 using the multiplication rule for independent events, right? If one of them fails, this does not mean that the other one is more likely to fail, so the events are independent. And now because we have two of them, we're multiplying 0.0235 by itself. This can be written as 0.0235 squared. And now the probability of A. Is going to be equal to 1 minus our previous result, 0.0235 squared. And now we are ready to perform the calculations. We're going to get 0.999. 448 which corresponds to the answer choice C. Thank you for watching.

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Key Concepts

Probability of Failure

Complement Rule

Independent Events

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