An interesting tweet from Fermat's Library proves that the average number of random values [0,1] that are needed to
Total > 1 is about $e$ (2.718...).
I don't get the proof, but I thought that a million trials in Mathematica should show something close to $e$ but I keep getting about 2.58 - I was hoping it would be an example of how you could get a clue about the proof by experimenting in Mathematica.
I suspect my coding skills are at fault, not the proof...
f[n_] := If[Total@RandomReal[1, n] > 1, n, f[n + 1]] Table[f, 1000000] // Mean // N