2014年東大前期文科第２問

RSolveではなく．．．，標本点を長さnのリストとして，標本空間S，好ましい事象F，確率測度を導入し，n=1,2,3,4でFの像（確率）を FindSequenceFunction に渡します．

FindSequenceFunction[
  Function[n, S = Tuples[{w, r}, {n}]; F = Select[S, Last@# === r &];
    Total@(Switch[#[[1]], w, (a + 2)/(a + 3), r, 1/(a + 3)]*
         Product[Switch[{#[[i]], #[[i + 1]]}, {w, w}, a/(a + 1), {w, r}, 1/(a + 1), {r, w}, 1, {r, r}, 0],
           {i, 1, Length[#] - 1}] & /@ F)] /@ Range[4], n] // FullSimplify