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Just a note

Notice that, provided the test has only 2 possible outcomes, the proportion of correct test results must equal one minus the proportion of wrong test results.
    If that is not immediately obvious, it is easy enough to prove.
  • Assume x results are positive and y results are negative.
  • Provided those are the ONLY possible outcomes, then x+y tests were performed.
  • The proportion of positive results is x/(x+y)
  • The proportion of negative results is y/(x+y)
  • Given that (x+y)/(x+y) equals 1
  • Then (x+y)/(x+y) - x/(x+y) = y/(x+y)
  • and (x+y)/(x+y) - y/(x+y) = x/(x+y)