basically its a binomial distribution where:
probability of event=.33
number of trials=16
number of successes=12
but instead of only 16, we want to 1500 trials and see if 12/16 ever occurs in those 1500. this is where i am hung up and can't find the formula i am looking for, tried google, wikipedia, even a statistics book...
if you consider that there are 93 independent trials in 1500 u can calculate it by taking (1-probability)^93, but this doesnt account for the fact that we arent looking at 93 sets of 16 trials, we are looking at 1500 trials so overlap can occur between the trials.