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Redundancy in Computer Hard Drives It is generally recognized that it is wise to back up computer data. Assume that there is a \(3 \%\) rate of disk drive failure in a year (based on data from various sources, including lifehacker.com). a. If you store all of your computer data on a single hard disk drive, what is the probability that the drive will fail during a year? b. 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 both drives will fail during a year? c. If copies of all of your computer data are stored on three independent hard disk drives, what is the probability that all three will fail during a year? d. Describe the improved reliability that is gained with backup drives.

Step by step solution

01

Calculate Probability of Single Drive Failure

The given rate of disk drive failure in a year is 3%. This can be represented as a probability of drive failure: \( P_1 = 0.03 \).

02

Probability of Two Drives Failing

Assuming the failures of two hard disk drives are independent events, the probability that both drives fail is the product of their individual failure probabilities.\( P_2 = P_1 \times P_1 = 0.03 \times 0.03 = 0.0009 \).

03

Probability of Three Drives Failing

If the failures of three hard disk drives are independent events, the probability that all three drives fail is the product of their individual failure probabilities.\( P_3 = P_1 \times P_1 \times P_1 = 0.03 \times 0.03 \times 0.03 = 0.000027 \).

04

Discuss Improved Reliability with Backup Drives

The improved reliability with additional backup drives is significant. With one drive, there is a 3% chance of failure. With two drives, the chance of both failing is reduced to 0.09%. With three drives, the chance is 0.0027%, which greatly enhances data security.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

disk drive failure rate

Disk drive failure rate is an important metric that helps us understand the reliability of a hard disk over time. In our exercise, we see that the failure rate is given as 3% per year. This means that out of 100 hard drives, you can expect about 3 of them to fail within a one-year period. By knowing the failure rate, we can calculate the probability of failure using the formula for probability, which is simply the failure rate itself. In this case, it is represented as \( P_1 = 0.03 \). This basic understanding helps in planning for better data storage solutions.

redundant storage

Redundant storage means storing the same data in more than one place to prevent data loss. Think of it as having multiple copies of a document. If one copy is lost or damaged, you still have the other copies. In our exercise, we saw examples of redundancy where data was stored on two or three independent hard drives. This method helps ensure that even if one drive fails, the data is still safe on the other drives. Redundant storage significantly improves the reliability of data preservation.

independent events

Independent events in probability mean that the occurrence of one event does not affect the occurrence of another. For example, if one hard disk drive fails, it doesn't mean that another hard disk drive will also fail. This principle is crucial in our exercise because we calculated the probability of two or three drives failing by assuming their failures are independent. The formula used for independent events is the product of their individual probabilities. So, for two drives, it was 0.03 multiplied by 0.03, and for three drives, it was 0.03 multiplied by 0.03 multiplied by 0.03.

backup reliability

Backup reliability refers to how dependable your backup systems are in preserving data. The more redundancy we have, the more reliable our backup. In our exercise, we calculated how adding more backup drives reduced the probability of total data loss. With just one drive, you had a 3% chance of losing data. Adding a second drive reduced this chance to 0.09%, and adding a third drive brought it down to 0.0027%. This shows that with each additional backup drive, the reliability of your data backup system greatly increases, ensuring your data is more secure.