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.
(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”