When I was a volunteer EMT, sometimes we would try to predict what type of calls we would get that day and how many times that call would happen. Each prediction for a specific type of emergency would depend on the time of year and if there were certain events, such as a music festival. For example, in the summertime with our station being the closest to the beach, we would try to guess how many calls there would be that day for a heat related emergency (ex: 4), and out of those, what would be the likelihood that our ambulance (perhaps ≤ 1) would get that emergency out of the 16 ambulances on call in the city. In a 12 hour shift on a weekend, just one ambulance can get up to 10 calls, each call averaging one hour (from first contact with patient to drop off at hospital and ambulance decontamination).
I don’t know about the people I worked with, but when attempting to make these predictions, I never used any math or calculations. I would make judgments and assumptions throughout the day based on the times between calls and our current location in the city (how close/how far from the beach, which hospital we were currently at). I suppose my sampling was non-random, specifically judgment sampling.
The type of sampling that would best be used is random sampling. In EMS, you never know what type of emergency call you will get, so I think simple random sample, or stratified sampling, would be the appropriate type of sampling.