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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.

Hubro
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    It's wise to start with the complement probability, that is: What is the probability that, during $n$ trials, the event has not occured? If the probability of the event is $p$ and all the trials are independent, then $$ P(\text{event not happened during n trials}) = (1-p)^n $$ After this, you can calculate $$ P(\text{event occurs at least one during n trials}) = 1-P(\text{event not happened during n trials}) $$ – Matti P. Mar 31 '20 at 07:33
  • @MattiP. Ah, I didn't notice you edited your comment. How come you didn't just post this as an answer? :) – Hubro Mar 31 '20 at 07:49

1 Answers1

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I finally figured it out... And considering how simple it turned out to be I'm ashamed it took me over 2 hours.

$$ f(x) = 1 - 0.9^x $$

Graph

(Is this correct? Or does it just approximate the correct answer close enough that I fooled myself)

Hubro
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