thanks Rohit, that is a start
n = 10;
t2 = Counts[Table[RandomInteger[], n] // Select[# > 0 &]];
(t2[[1]] - n/2)/n // N
now I would like to repeat this process to create a list where n increases, something like the following but it doesn't work
Table[
t2 = Counts[Table[RandomInteger[], n] // Select[# > 0 &]];
(t2[[1]] - n/2)/n // N, n = 10^i, {i, 0, 10}]