The estimates here are based on statistics from three places that have reported detailed data on Covid infections by vaccination status: Utah; Virginia; and King County, which includes Seattle, in Washington state. All three are consistent with the idea that about one in 5,000 vaccinated Americans have tested positive for Covid each day in recent weeks.

The chances are surely higher in the places with the worst Covid outbreaks, like the Southeast. And in places with many fewer cases — like the Northeast, as well as the Chicago, Los Angeles and San Francisco areas — the chances are lower, probably less than 1 in 10,000. That’s what the Seattle data shows, for example. (These numbers don’t include undiagnosed cases, which are often so mild that people do not notice them and do not pass the virus to anyone else.)

Here’s one way to think about a one-in-10,000 daily chance: It would take more than three months for the combined risk to reach just 1 percent.