47. Suppose that a company assigns an extra digit to every employee Social Security number by appending a 0 if the sum of the digits is even and a 1 if the sum is odd. If a 2 were mistakenly read as a 7, would the error be detected? What if a 2 were mistakenly read as an 8? Try a few other experiments with single-digit errors. (For experiments, you can use three-digit numbers instead of nine-digit numbers.) Determine which errors are detected by this method. Explain your reasoning. Approximately what percentage of errors is detected by appending the extra digit?
47.
The mistake of reading a 2 as a 7 is detected because the sum of the digits of the incorrect number would be odd. The mistake of reading a 2 as an 8 is not detected because the sum of the digits of the incorrect number would remain even. An error is detected when an odd digit is misread as an even one (or vice versa) because the sum of the digits changes from even to odd (or vice versa). Approximately 50% of errors are detected.