Confidence level calculation

[Hyperbar00]

Greetings everyone,

I was looking at the Uranium processing page on the game wiki : https://wiki.factorio.com/Uranium_processing especially the confidence level calculation and I found myself interested by the formulas used to obtain these results.
Could anyone provide them and why not the different steps and values please ?

Thank you in advance

[DaveMcW]

POISSON.DIST() Excel function

failure_chance = POISSON.DIST(required_number_of_successes, success_chance * number_of_events, TRUE)

failure_chance = POISSON.DIST(40, 0.007 * 7000, TRUE)

failure chance for 7000 cycles = 10.98%

[DaveMcW]

Looking at the wiki history, the table and graph were obtained by using a simple ratio. That is the wrong way to do it.

[Hyperbar00]

Thanks A LOT !

I was trying to use Binomial Distribution and quickly noticed that it wasn't the right way because my result ended being undefined upon reaching high values.
So I couldn't figure how to get the job done until you gave me the answer. A huge thank you

I was looking for this formula because of the Realistic Fusion mod which gives a 0.02% chance to get 1 Deuterium so I wanted to get some probabilities and stuff in the same fashion as the factorio wiki.
So if I got the calculations right, with a 0,02% chance to get one, I roughly need 23700-23800 cycles in order to get a 95% probability ?

[nesklein]

POISSON.DIST() Excel function

failure_chance = POISSON.DIST(required_number_of_successes, success_chance * number_of_events, TRUE)

failure_chance = POISSON.DIST(40, 0.007 * 7000, TRUE)

failure chance for 7000 cycles = 10.98%

It really helped. Thank you very much.