The following function CoinSim[n] generates a simulation of a fair coin being tossed n times:

CoinSim[n_]:=Module[{population,Pr,sim},
population=Table[RandomInteger[],{n}];
Pr[k_]:=Table[Mean[Take[population,i]],{i,1,k}];
sim=Manipulate[ListPlot[Pr[j],PlotRange->{{0,Automatic},{-.1,1.1}},PlotStyle->{PointSize[0.015]},AxesLabel->{TraditionalForm["n"],TraditionalForm["(Subscript[f, n])(H)"]}],{{j,1,TraditionalForm["n"]},1,Length[population],1}];
sim]

CoinSim[1000]