As a single mother, Beatrice Duran never imagined that she would get involved in politics. When she moved to Las Vegas in 1985, her focus was on keeping “a solid job” as a food server to provide for her young daughter and, later, her son.

Opportunities to become involved in public life felt out of reach.

Now, her appointment on Tuesday to the Nevada State Assembly, along with that of another woman, will make female lawmakers the majority in the state capital — the first time that has happened in the nation’s history. Ms. Duran and Rochelle Thuy Nguyen, both Democrats, were selected by the Clark County Board of County Commissioners to fill recently vacated seats.

“This is going to show more women that we can do it,” Ms. Duran, 55, said.

With Ms. Duran and Ms. Nguyen’s arrival, women will hold 32 of 63 seats in the Nevada Legislature when the next session begins in February, about 51 percent. No state house in history had ever crossed the 50 percent mark, according to the Center for American Women and Politics at Rutgers University.

New Hampshire previously had majority women representation in the state Senate, but women were not the overall majority in the Capitol.