Error Rate Calculations
The purpose of this paper is to analyze the following question.
Given an record that where the original no longer exists, but some number of copies
have been made of the original, what is the likelihood that the original will be preserved
somewhere in the first generation copies?
An analysis of this question can be made from the field of probability and statistics.
ASSUMPTIONS
 Assume that the error rate is completely random. This is not likely since some types of
errors are more likely than others. These types errors are well documented.
 Only the first generation copies are analyzed in this paper.
VARIABLES USED
 M is the number of characters in the record
 N is the number of copies of the original record
 P is the error rate in the copies
EQUATIONS

 M*P is the number of errors per copy
 M*N*P is the total number of errors
 PN is the probability that all copies will have an error in a particular character
 M*(PN) is the probability that all copies will have an error in any same character
EXAMPLES
Example #1:
M=100,000 characters
N=10 copies made of the original record
P=.001 error rate (0.1%)
 100 errors per copy
 1000 total errors
 .00110 = 1x1031
 (1x105) x (1x1031) = 1x1026
Example #2:
M=100,000 characters
N=2 copies made of the original record
P=.001 error rate (0.1%)
 100 errors per copy
 1000 total errors
 .0012 = 106
 105 x 106 = 1/10
ANALYSIS OF EXAMPLES
 Example #1 shows a "best case" situation. In this example the original had 10
copies made. The probability is very small that there are multiple errors in the same
character. The probability, although small, is not equal to zero.
 Example #2 shows a one in ten chance that the original was lost for a single character.
The chance that more than one character from the original was permanently lost is much
smaller. One single character out of a record of over 100,000 is not a lot of error.
CONCLUSIONS
If there was only one copy of the original made and there were any errors in the copy,
there is no way that the original can be restored, as it is permanently lost. The worst
case scenario still shows a very small error rate.
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