Probability calculation with an infinite variable? Let's say i have a RNG(random number generator) that generates a number 1-10, if i guess any number the chance for it to be true is 10%. Now let's say i have an RNG that generates a number with any value, yes i know this is unrealistic but this is just hypothetical, No what if i guess a random number? What will the chance of me being correct be? The RNG is going to generate some number, so there is a correct answer, but how would one find the probability? 1/infinity*100 wont even work since infinity isn't even a number and something like that would give you 0. And since there is a correct answer, no matter how small the chance of being corrext is it's still there, right? or no?
 A: A very important aspect of the RNG you don't explicitly mention is its "distribution", how likely it is to choose each number in turn. This is important to specify, since it might do something strange like pick lower numbers more often, or pick even numbers twice as much as odd numbers.
Since you're presuming that it has a $10\%$ chance to output any particular number between $1$ and $10$, you presumably have the uniform distribution in mind, i.e. every number in range should be just as likely as any other.
An RNG ranging over any integer value, no matter how large, cannot have a uniform distribution for basically the reason you mention: you'd have to divide the total probability of $100\%$ across infinitely many numbers, while still having all those infinite probabilities add up to $1$. That's impossible, because the only options are $0$, in which case adding up infinitely many gives you $0$ (but needs to give you $1$) or something larger than $0$, in which case adding up infinitely many gives you $\infty$, which isn't $1$ either.
For a more formal and general answer, you can also see this thread.
A: I believe that the event of choosing the correct number is a possible event, but it's probability is still 0. Watch this 3B1B video: https://www.youtube.com/watch?v=ZA4JkHKZM50
