built in symbols - Pop-up documentation for "The new function of the day"

The Wolfram Language has more than 5000 built-in functions and constants.

functionslist = Flatten[
   Names[#] & /@ Flatten[
     {# <> "*", "$" <> # <> "*"} &
      /@ CharacterRange["A", "Z"]
     ]
   ];
Length @ functionslist

5689

OK, 5689 have documentation in Mathematica 10.3, to be more precise. In order to keep up with that, I would like to pick randomly a function documentation to refresh.

SystemOpen["paclet:ref/" <> RandomChoice[functionslist]]

But I would like to refresh new functions more often than old ones.

SystemOpen["paclet:guide/SummaryOfNewFeaturesIn103"]

How can we implement a "New function of the day" function that focuses on functions new to the current version?

Bonus if it picks from all functions with decaying probability as a function of "age".

_{Code adapted from this question.}

Answer

Here is an alternative procedure using EntityValue[] and Dataset[]. The idea is to build a Dataset[] containing function names and the version numbers they were introduced in, and then use a query to pull all the names that are new in a particular version. One can then pick any of these names randomly. A way to bias newer functions over older ones is to use RandomChoice[] on the list of version numbers, with each version number being its own weight.

$versions = {1, 2, 2.2, 3, 4, 4.1, 4.2, 5, 5.1, 5.2, 6, 7, 8, 9,
             10, 10.1, 10.2, 10.3};


symtable = Dataset[AssociationThread[{"Name", "VersionIntroduced"}, #] & /@
           EntityValue["WolframLanguageSymbol", {"Name", "VersionIntroduced"}]];

randomHelpPage := With[{version = RandomChoice[$versions -> $versions]},
         SystemOpen["paclet:ref/" <> RandomChoice[Normal[
                    symtable[Select[#VersionIntroduced == version &], "Name"]]]]]

Button["Random WL Function", randomHelpPage]

This should now function in a similar manner to Jason's solution.