L[p_,x_]:=If[x≤p,1,0]

Y[p_,n_]:=Sum[L[p,Random[]],{k,1,n}]

p=0.3; n=10;

P[m_]:=ListPlot[{Table[{k,(BinCounts[Table[Y[p,n],{k,1,m}],{0,n+1,1}]/m)[[k+1]]},{k,0,n}],Table[{k,Binomial[n,k] p^k (1-p)^(n-k)},{k,0,n}]},Filling->Axis,PlotStyle->PointSize[Large],PlotLabel->m,Frame->True,PlotRange->{0,0.4}]

For [k=1,k<5,k++,Print[P[10 10^k]]]