It’s not P(E) x1825 that makes no sense because the probabilities are independent. It’s 1 - (1 - P(E))^1825 – your maths would imply that a 1/1000 chance had a 100% probability of happening after 1000 attempts, which is not how independent probabilities work.
Anyway I’d probably go for it if it were, like, 1/100,000, giving a probability of the bad thing happening once over 5 years at just under 2%
I just remembered I hadn’t tried to write anything in J for like a year so I had a go at seeing how far the approximation was from the real values and got:
So it looks like the ratio probably converges as you increase n (these results are for 1, 1/10, 1/100 etc) but that x1825 is always higher and starts off wildly off. But these numbers are probably mad squiffy because floating point yadda yadda.
Edit again: oh yeah. Binomial expansion. Once the negation of your probability gets very close to 1 the initial coefficient will absolutely dominate. Proof left for reader.
It’s not
P(E) x 1825that makes no sense because the probabilities are independent. It’s1 - (1 - P(E))^1825– your maths would imply that a 1/1000 chance had a 100% probability of happening after 1000 attempts, which is not how independent probabilities work.Anyway I’d probably go for it if it were, like, 1/100,000, giving a probability of the bad thing happening once over 5 years at just under 2%
I just remembered I hadn’t tried to write anything in J for like a year so I had a go at seeing how far the approximation was from the real values and got:
So it looks like the ratio probably converges as you increase n (these results are for 1, 1/10, 1/100 etc) but that
x 1825is always higher and starts off wildly off. But these numbers are probably mad squiffy because floating point yadda yadda.Edit again: oh yeah. Binomial expansion. Once the negation of your probability gets very close to 1 the initial coefficient will absolutely dominate. Proof left for reader.