I can't tell if we're disagreeing or just at cross purposes. In the code above the random number is uniform(0,1), the standard random number in most languages.

I can't tell if we're disagreeing or just at cross purposes. In the code above the random number is uniform(0,1), the standard random number in most languages. So each individual death is Bernouilli, although you don't need to know the word Bernouilli. Then this leads to a binomial distribution for a hospital as a whole. But the binomial assumption doesn't need to be known or explicitly built into the model. It's effectively an emergent property of the individual deaths.