random percent upper bounce algorithm

I would like to find the upper bound of a random percent

For example: if probability of something will happen = 20% then upper bound will be

YES NO NO NO NO YES NO NO NO NO

It will ensure that the chance will be always >= 20%

to design something like for 1 user is quite simple but what happen if we have 2000 submit at a time. what is the best way to get upper bound if there are large number of request.