RALEIGH, N.C. (WNCN) — What are the chances everyone in a random group of people has been vaccinated for COVID-19?
It may be lower than you think.
“There still is a very high chance that if you get together in a group, not everyone’s going to be vaccinated, even in places that have high proportions,” said Paul Delamater, a professor at the University of North Carolina and an expert in health geography whose website nc-covid.org tracks pandemic trends.
For a case study, look at Dare County near the coast.
According to his website, that county has the state’s highest rate of adults getting at least one shot — 77 percent, after Wednesday’s update.
But if you gathered a random group of 10 adults from that county, Delamater calculates the chances that everyone in that group being vaccinated at just 2.3 percent. For a group of 25, he says it’s effectively zero.
In the other 99 counties where the uptake rates of the vaccine is lower, those odds drop even further.
“It would be fair to assume that the percent chance that everyone at a (random) group of 10 is vaccinated is near zero if the county is down around like 50 percent” partially vaccinated, Delamater said.
Why so low? It has to do with how probability works.
In a way, it’s the opposite of the famed birthday paradox — in a group of 23 people, the chances that at least two of them share a birthday are 50-50. It exceeds 99 percent in a group of 70.
It’s easy to figure out the chances that one random person in a county has been vaccinated — that’s just the overall percentage. But — like flipping a coin several times and having it land on heads every time — it becomes increasingly less likely that as the size of the group increases, every additional person added to it is also a member of the subset of vaccinated people.
“You have to think of this as drawing people at random out of a population,” Delamater said.
It’s important to understand those chances as the state moves through the reopening process, with groups of 100 people indoors and 200 outdoors now permissible under Gov. Roy Cooper’s end-of-April executive order.
“I think it just underscores how important it is to get those numbers up as high as possible and to get people vaccinated, just so we can get back to normal,” Delamater said. “So we can gather in these groups and not be worried that someone there is still susceptible to COVID.”
Of course, your risk of catching COVID-19 drops significantly once you’re fully vaccinated, as just over half of adults across the state are, according to the state Department of Health and Human Services.
Those vaccination rates are having an effect on the COVID-19 case counts, with the nc-covid.org risk maps looking markedly less orange and red now than they were six months ago.
“The chances that there’s a person who’s currently infectious is pretty low right now across the state,” Delamater said.