Since the site is down, let's DIY just for fun.
@Deleted member 18037, let's use your example of a reported infection rate of 1.2 percent. We'll assume 50 kids in the gym.
To find the probability that any person (one or more persons) in the gym is infected, we first need to find the probability that no one is infected. This is the probability of a repeated event: the probability that the first person, and the second, and the third, and so on all the way through the fiftieth person, is not infected. To do this, we take the probability that any given person is not infected (.988 if the infection rate is 1.2 percent) and raise it to the power of the number of people in the group. So we raise .988 to the 50th power, which gives us .547. So given an overall infection rate of 1.2 percent, there is a 54.7 percent chance that no one in a group of 50 is infected. Subtract from 100 percent, and we see that there is a 45.3 percent chance that anyone (one or more persons) in that same group is infected. If there are 100 people in the group, the probability that no one is infected falls to .299, and the chance of someone's being infected rises to 70.1 percent. So we can see that even with a low overall infection rate, the probability that someone in a large group is infected is quite high.
If infections are undercounted, the risk of an infected person's being present is greater. If there are 10 times as many actual infections as reported infections, the infection rate is 12 percent. In that case, the probability that a 50-person group includes at least one infected person is greater than 99 percent.
@gymgal, that's probably why you are seeing such high numbers if you are looking at the county-level estimates--the county-level estimates assume a true infection rate 10x the reported rate. The tool only seems to use the range of assumptions (1x, 5x, 10x) at the state level.
Fun, right?