No distribution needed - 46% is 100% - (100% - 5%)^12, as if you were rolling a die 12 times. The population is large enough that the effect of removing 11 people from it should be negligible.
This is not "no distribution", this is a binomial distribution - where every one of n items has an equal probability p of being a certain result. You are correct that in this case removing the 11 people from the population is negligible, thus p remains the same.
