Probability of sample minimum below a certain value I have a list of 1000 songs with their bpm (beats per minute). If I were to sample 30 songs, is there a way to find the probability that the sample minimum is below a certain value like 100 bpm?

"Sample minimum below a value" $T,$ say, means "all outcomes in the sample are $T$ or greater."  I will refer generally to "$T$ or greater" as your criterion.
Suppose $M$ of the $1000$ songs do not satisfy your criterion: that is, their bpm value is $T$ or greater.  You will have to count them: there is no general shortcut to finding $M$ based on $T.$

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*When sampling without replacement, $\binom{M}{30}$ samples out of all $\binom{1000}{30}$ equally likely samples have no outcomes meeting your criterion.  Therefore the chance that at least one outcome does meet your criterion is $$1 - \frac{\binom{M}{30}}{\binom{1000}{30}} = 1 - \frac{M(M-1)\cdots(M-30+1)}{1000(999)\cdots(1000-30+1)}.$$


*When sampling with replacement, $M^{30}$ samples out of all $1000^{30}$ equally likely samples have no outcomes meeting your criterion.  Therefore the chance that at least one outcome does meet your criterion is $$1 - \frac{M^{30}}{1000^{30}} = 1 - \left(\frac{M}{1000}\right)^{30}.$$
