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If we would have a perfect random decimal number generator, so a one that generates from: 0 1 2 3 4 5 6 7 8 9 - than what would be the chances to get ex.: 1 ? or 2? or 3? and so on..

Question: would it be the same, so 10% chance? Or it depends on how many samples do we generate?

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    This isn't clear. Yes, a uniform random digit generator would, by definition, return each digit with probability $\frac 1{10}$. But of course a sample might not reflect that...you might get $6$ ten times in a row. You probably won't, but you might. So...what exactly are you asking? – 2017-01-12
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    thanks for the info, the real question is that how many samples do I need to assume that the chances were 10% per number? are there any formulas if we know that we are generating the following numbers: 0 1 2 3 4 5 6 7 8 9. ex.: I need to generate 1 trillion numbers to get 99.9% ratio for the most and least often occuring number? – 2017-01-12
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    You should edit the question to reflect your intent. But your question is still not precise enough: it is perfectly possible to randomly generate a trillion $6's$ in a row...it's just not likely. Usually one asks this sort of thing in terms of [Confidence Intervals](https://en.wikipedia.org/wiki/Confidence_interval)...something like "how big a sample do I need to ensure that no digit occurs $11\%$ or more of the time with probability at least $.95\%$ ?" I made up the numbers of course, but that's the sort of thing that will have a well defined answer. – 2017-01-12
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    created https://math.stackexchange.com/questions/2096315/what-is-the-formula-for-the-sample-size-to-check-that-random-generated-decimal-n for it, thanks! – 2017-01-13

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"Perfect random" by itself does not really mean anything. "Perfect random uniform" would mean that every number the generator produces independently has probability $1/10$ to be any of those 10 digits. Usually, if unspecified, distributions are usually understood to be uniform, though. (Just like we generally assume coins and dice in probability thought experiments to be fair.)

Of course, if we produce more numbers the chances of any one number appearing go up; for example, the probability of a 1 with two generated numbers is $19/100$. But for each number generated taken on its own, the probability is still $1/10$, so even if you generate two numbers, the probability of the second one being a $1$ is still $1/10$, no matter what value the first number had.