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Probability that feel like guarantee

Trivia · proposed by @vipproaccout 1333
Suppose an event has probability $\dfrac{1}{n}$ of occurring. If the corresponding trial is performed $n$ times independently, what is the probability that the event occurs at least once (as $n \to \infty$)?
A$100\%$ B$\approx91.3\%$ C$\approx87.4\%$ D$\approx63.2\%$ E$\approx36.8\%$