Let's say there's a 1/10 chance of something happening.
Given 1 chance, there's a 0.1 chance of the thing happening.
Given 2 chances, there's a 0.1 + (0.9 * 0.1) chance of the thing happening.
Given 3 chances, there's a ... Help!
Is there any way to plot this, such that given X chances, the chance of the thing happening at least once is Y?
f(x) = ...
I have also tried for a good hour to graph the opposite, i.e. what are the odds that given X chances, the thing doesn't happen a single time. My uneducated brain can't think of a way to graph any of these without referring to the result of f(x-1), which is not allowed in the graph editor I'm using.
I finally figured it out... And considering how simple it turned out to be I'm ashamed it took me over 2 hours.
$$ f(x) = 1 - 0.9^x $$
(Is this correct? Or does it just approximate the correct answer close enough that I fooled myself)