P[n_]:=ListPlot[BinCounts[(1+RandomInteger[5,n]),{1,7,1}]/n,Filling->Axis,PlotRange->{{0.5,6.5},{0,0.5}},PlotStyle->PointSize[Large],PlotLabel->n,Frame->True]

For [k=1,k<6,k++,Print[P[10 10^k]]]