区间命中概率

单个样本落入区间 $[0.5,0.55]$ 的概率为区间长度 $p=0.05$。

生成 $n$ 个独立样本，至少一个落入区间的概率为

$$1-(1-p)^n=1-0.95^n.$$

要求 $1-0.95^n\ge 0.95$，即

$$0.95^n\le 0.05 \Rightarrow n\ge \frac{\ln 0.05}{\ln 0.95}\approx 58.4.$$

取最小整数得 $\boxed{n=59}$。

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英文解析

The probability that a single sample falls into the interval $[0.5,0.55]$ is the interval length $p=0.05$.

Generate $n$ unique samples with at least one probability of falling into the interval

$$1-(1-p)^n=1-0.95^n.$$

Request $1-0.95^n\ge 0.95$ i.e.

$$0.95^n\le 0.05 \Rightarrow n\ge \frac{\ln 0.05}{\ln 0.95}\approx 58.4.$$

The smallest integer is $\boxed{n=59}$.