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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.