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Chapter 13: Problem 5

Lost Internet Sites. Intemet s?tes often vanish or move so that references to them can't be followed. In fact, \(13 \%\) of Internet sites referenced in major scientific journals are lost within two years after publication. \({ }^{4}\) If a paper contains seven lntemet references, what is the probability that all seven are still good two years later? What specific assumptions did you make to calculate this probability?

Short Answer

Expert verified
The probability that all seven are still good is approximately 0.434, assuming independence among references.

Step by step solution

01

Understanding the Probability

First, we need to determine the probability that a single internet site remains accessible after two years. Given that 13% of internet sites are lost, this means 87% are still accessible. Therefore, the probability that one site is still good (accessible) after two years is 0.87.
02

Defining the Event

We need to find the probability that all seven internet sites referenced in the paper are still accessible after two years. This scenario can be modeled using the binomial probability formula or simply the concept of independent events, where each site independently has a 0.87 probability of remaining accessible.
03

Calculating the Combined Probability

Since each internet site remains accessible with a probability of 0.87 (assuming independence), the probability that all seven sites remain accessible is given by multiplying the individual probabilities: \( (0.87)^7 \).
04

Performing the Calculation

Calculate \( (0.87)^7 \) to find the probability. Using a calculator, \(0.87^7 \approx 0.433908\).
05

Identifying Assumptions

The calculation assumes that the likelihood of each internet site being accessible after two years is independent of the others, meaning the status of one link doesn't affect another. Furthermore, the probability of remaining accessible remains constant over the two-year period.

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Key Concepts

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

Independent Events
In probability theory, independent events are those where the outcome of one event does not affect the outcome of another. This concept is crucial when considering occurrences such as internet references remaining accessible.
For instance, in the exercise we are discussing, the accessibility of one internet site after two years is independent of another. This means if one site stays accessible, it has no impact on whether another site will behave similarly.
  • This allows us to calculate the probability of multiple events (such as several internet sites) by multiplying their individual probabilities together.
  • It's essential to check that the assumption of independence is reasonable when applying it to real world scenarios.
So in the example, for each of the seven sites referenced in the paper, knowing that one remains accessible gives no information about whether others will also be accessible.
Probability Calculation
Probability Calculation involves determining the likelihood that an event or a series of events will occur. In our case, we calculated the probability that all seven internet site references are still good after two years.
Here is how we proceeded:
First, identify the probability of a single event, which is 0.87, as each site has a 87% chance of remaining accessible.
  • To find the probability that all seven sites remain accessible, we multiply the probabilities of each site: \((0.87)^7\).
  • This method is valid because of the assumption that each event (site reference remaining valid) is independent.
This independence means we can perform the multiplication, resulting in a combined probability of approximately 0.433908.
Scientific Journals
Scientific journals often reference internet sites for various reasons, such as citing online studies, tools, or databases. However, the accessibility and longevity of these references can be uncertain.
  • Research shows that 13% of sites referenced in scientific journals become inaccessible within two years, which can pose issues for scientists and researchers relying on these sources for data or further information.
  • This fact heightens the importance of carefully selecting references and potentially storing vital information offline or through more stable online archives.
Researchers must therefore ensure their findings and supporting evidence remain accessible long-term, maintaining the integrity of their work and aiding future research.
Internet References
Internet references in academic and professional disciplines serve as a bridge to a wealth of online information that supports and enriches the substance of papers and publications.
With 13% of these sites potentially disappearing in just two years, scholars must be aware of strategies to mitigate the risk of "link rot," which is when these links become unavailable.
  • Options to address this include using digital object identifiers (DOIs) that can persistently link to resources, turned into new or archived locations if the original is lost.
  • Library services or digital archiving like web citations, can also offer longer-lasting solutions to ensure continued accessibility.
This ensures that the valuable content remains accessible, preserving the link between published theories and their supporting data.

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