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[I don’t know how to properly write the notation, so any help is appreciated.]

There is a device that generates random integer numbers. The number of possible values that it can generate is x. For ex., if a device can generate any number between 4221 and 5220, inclusive, we say that x=1000.

If the device generates a number that it already generated in the past, we have a “collision”.

Given x, what is the probability for a collision after generating n numbers?

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    This is essentially the birthday probnlem, only with $x$ days instead of $365$ https://en.wikipedia.org/wiki/Birthday_problem As written in the article, the probability is approximately $1 - \exp(-n^2/(2x))$, if $n$ is small compared to $x$. – 2017-01-26
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    @Dominik: Thanks for your answer. I try to calculate where x=32^11, and n=1000. I pasted the text 1 - e(-(32^11)^2 ÷ 2000) to google scientific calculator, and it gives me a very big number, with a lowercase e. It also have EXP, E and e, so I'm confused. Can you explain to me which text should I paste to the calculator? – 2017-02-12
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    You've changed $x$ and $n$ in your calculations. The correct value is very small. [See Here](http://www.wolframalpha.com/input/?i=1-exp(-1000%5E2%2F(2*32%5E11))). – 2017-02-12
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    @Dominik: Thanks a lot! – 2017-02-12

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