The Omicron variant of the coronavirus has been so contagious that it may have seemed a foregone conclusion that if one person in a household became ill, other people living there would catch the virus, too.

But that turns out to be less certain: A small study of households by the Centers for Disease Control and Prevention released on Friday found that when the first person infected wore a mask and stayed in a separate room at least part of the time, the risk of other household members contracting the virus became markedly lower.

Vaccinated people who became infected were also considerably less likely than unvaccinated people to spread the virus to other members of their households.

Still, the study highlighted just how aggressively the Omicron variant had spread within a home, especially among people living with children under 5 who tested positive. Those children, who are not yet eligible for vaccines and often need to be in closer contact with their parents or relatives, spread the virus to 72 percent of household contacts identified in the study — the highest rate of any age group, the C.D.C. said.

“These findings further highlight young children’s potential contribution to household transmission,” C.D.C. scientists wrote in the report.

Federal regulators are waiting for data on how well three doses of the Pfizer-BioNTech coronavirus vaccine work in children under 5 before deciding whether to authorize the vaccine for that age group.

The C.D.C. study was based on 183 households across four states where someone became infected with the Omicron variant from November to early February. After interviewing members of the households about their vaccination and infection histories, any precautionary measures in the home and whether they had tested positive or become ill, C.D.C. scientists determined that the variant had spread in roughly two-thirds of the households they identified.

But when the first infected person was fully vaccinated, only about 44 percent of household members developed Covid, compared with 64 percent when the infected person was unvaccinated, the study said.

And when the original infected household member stayed in a room alone at least some of the time, only 41 percent of other members of the household became infected, compared with 68 percent in situations without isolation. Masking by the infected person helped, too, reducing the likelihood of transmission to 40 percent from 69 percent.

Determining the precise risk of the virus spreading in a home was difficult, the study’s authors noted. They excluded situations where it was unclear who had first developed Covid, and did not do the genetic sequencing necessary to know for certain that people had caught the virus from the infected person in their home rather than at other gatherings.