[TIP] Math question - related to testing, not python-specific

[Marc Tardif]

Assuming the attempts are independent, the number of errors E out of
t trials follows a binomial distribution

  E ~ Bin(t, p)

The probability of an error occurring at least once is

  P(E >= 1) >= q

which is equivalent to

  1 - P(E = 0) >= q

which simplifies to

  1 - nC0 * p^0 * (1 - p)^(t - 0) >= q
  (1 - p)^t <= 1 - q
  t * ln(1 - p) <= ln(1 - q)
  t <= ln(1 - q) / ln(1 - p)
  t >= ln(1 - p) / ln(1 - q)

For example, if p = .5 and you want q = .01

  t >= ln(1 - .5) / ln(1 - .01)
  t >= 69

* Dan Stromberg <dstromberglists at gmail.com> [2020-02-20 12:40 -0800]:
> If a transient error fails with probability p for one invocation of a test,
> how many times t do you have to run the test to have probability q of an
> undetected, continued failure getting missed?
> 
> By a "transient error", I mean a test that fails p*100 percent of the time
> with the same inputs - usually caused by a race condition.
> 
> I think I remember enough discrete math to formulate the question, but I
> don't remember enough to answer it for myself :-S

-- 
Marc Tardif <marc at interunion.ca>
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