If I already have n random numbers(between 0-100), what's the duplication probability when I random next number?
This is a chart represent probability(0-100%) of this question when n is between 1-500. I don't sure what is formula that represents this chart. Or it's just normal characteristic of pseudo random that I use.
PS. I quite confuse this problem with birthday problem. But I know the probability between 2 cases are totally difference.
We make an interpretation of your problem. We are choosing $n+1$ times, with replacement, a number from the set $\{0,1,2,\dots,100\}$, where all numbers are equally likely to be chosen.
Let random variables $X_1, X_2,\dots, X_n,X_{n+1}$ be the sequence of numbers chosen. We want the probability that $X_{n+1}$ is different from all the $X_i$, where $1\le i\le n$.
Suppose that $X_{n+1}=x$. Then for any $i$ such that $1\le i\le n$, we have $$\Pr(X_i\ne x)=\frac{100}{101}.$$ Thus by independence the probability that $X_i\ne x$ for all $i$ such that $1\le i\le n$ is equal to $$\left(\frac{100}{101}\right)^n.$$