I have three clinics that are testing for Zika virus. However, we know that the volume of patients each clinic tests varies, but we do not know by how much. What we do know is the proportion of positives that are identified in each clinic, i.e., the first clinic has identified 20% of all positives across the three clinics, the second 30% and the third 50%. Now we know there are 100 new cases but we do not know which clinics identified them. We can guess that 20 are from the first clinic, 30 from the second clinic, etc, but what if I want to know the likelihood that only 5 positives came from the first clinic? I know I can run a Monte Carlo simulation to figure this out, but I was wondering if there was a distribution that describes this.

I have three clinics that are testing for Zika virus. We know the proportion of positives aggregated across all clinics, i.e., the first clinic has identified 20% of all positives across the three clinics, the second 30% and the third 50%. Now we know there are 100 new cases but these proportions change with respect to previous cases, i.e., they are now 10% 50% and 40%. Is there a distribution that can tell me if these proportions are significantly different than would be expected given the original proportions? I have run a Monte Carlo simulation to figure this out, but I was wondering if there was a distribution that describes this.