[kchamplewski]

The fact that the math here is wrong is quite concerning. Probabilities are not additive - 1 in 6 dice rolls will produce a 5, it doesn't mean if I roll 6 times I am guaranteed a 5.

[Someone]

For small probabilities, approximating

  (1-p)^n

by

  1 - n × x

is absolutely fine. For example

  (1-0.00002)^5 = 0.999900004

Rounding gives you that “one in 10,000”

[caf]

Adding the probabilities is a good enough approximation when the probabilities and number of trials are very low, though - as in this case. The true value for at least one failure in 5 trials with an individual 1/50000 probability of failure is 1/10000.4 rather than 1/10000, but it seems clear that the original 1/50000 isn't that precise anyway.