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## Minimum of Random Subsets

Let $S =${$1,2,\dots,n$}. Let $A,B$ be two random subsets of $S$. Let $\min(A)$ denote the minimum number in the set $A$.

• What is the probability that $\min(A)= \min(B)$ ?

• Evaluate this probability as $n$ tends to infinity.

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