# a simple question about probabilities

In a game a player has a probability of $\frac{1} {N}$ to win, where $N \in {\Bbb N}$. It´s possible to calculate the probability of at least one win, after $k$ tries?

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Yes, the probability of at least one win is 1 minus the probability of no wins: $1-\bigl(1-{1\over N}\bigr)^k$ (assuming independence between games).
In general, you use $P(A)=1-P(\text{not }A)$. The complement of (the "not" of) "at least one" is "none".