4. Probability
Multiplication Rule: Independent Events
1:08 minutesProblem 4.2.25a
Textbook Question
Redundancy in Computer Hard Drives It is generally recognized that it is wise to backup computer data. Assume that the following refer to use of Western Digital model WD60EFRX hard drives, which have an annual failure rate of 3.66% (based on data from Backblaze, Inc.).
a. If you store all of your computer data on a single hard drive, what is the probability that the drive will fail during a year?
Verified step by step guidance1
Step 1: Understand the problem. The problem asks for the probability that a single hard drive will fail during a year. The annual failure rate of the hard drive is given as 3.66%, which can be expressed as a decimal (0.0366).
Step 2: Recall the concept of probability. The probability of an event occurring is the likelihood of that event happening, expressed as a value between 0 and 1. In this case, the failure rate (3.66%) directly represents the probability of failure for a single hard drive in a year.
Step 3: Convert the percentage to a decimal. To use the failure rate in calculations, divide the percentage by 100. For example, 3.66% becomes 0.0366.
Step 4: Interpret the result. The value 0.0366 represents the probability that the hard drive will fail during a year. This is the final probability for this specific scenario.
Step 5: Note that no further calculations are needed since the failure rate is already provided as the probability. Ensure you understand that this probability applies to a single hard drive over the course of one year.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Probability of Failure
The probability of failure refers to the likelihood that a specific event, such as a hard drive malfunction, will occur within a given time frame. In this context, the annual failure rate of 3.66% indicates that there is a 3.66% chance that the hard drive will fail within one year. Understanding this concept is crucial for assessing risk and making informed decisions about data storage.
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Annual Failure Rate
The annual failure rate (AFR) is a statistical measure that quantifies the percentage of devices expected to fail over the course of a year. For the Western Digital model WD60EFRX hard drives, an AFR of 3.66% means that, on average, approximately 3.66 out of every 100 drives will fail each year. This metric helps users evaluate the reliability of storage solutions and plan for data redundancy.
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Data Redundancy
Data redundancy is a strategy used to protect data by storing copies in multiple locations or on multiple devices. This approach mitigates the risk of data loss due to hardware failure, as it ensures that if one hard drive fails, the data can still be accessed from another source. Understanding data redundancy is essential for effective data management and safeguarding against potential failures.
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