Nevada’s Legislature has one of the highest percentages of women in the country, at almost 40 percent. Here are the members of its State Senate and Assembly:

Members of the Nevada Legislature on April 26, 2017. Composite image by The New York Times using photographs by Bob Cook, Cooks Photography.

A record number of women won Nevada’s primaries in June. And there is now a possibility for the Legislature to have more women than men, which would be a first in United States history. Of the states that have had primaries so far, at least eight more have a shot at reaching or surpassing the 50 percent mark in November.

Where women could make up at least half the state legislature Current share of women Potential after the general election 38% 65% Nevada Maine Colorado Oregon Maryland California North Carolina Illinois South Dakota 34 62 38 54 33 53 33 52 25 50 25 50 36 50 19 50 0 50 100% Current share of women Potential after the general election Nev. Maine Colo. Ore. Md. Calif. N.C. Ill. S.D. 38% 65% 34 62 38 54 33 53 33 52 25 50 25 50 36 50 19 50 0 50 100% Current share of women Potential after the general election Nev. Maine Colo. Ore. Md. Calif. N.C. Ill. S.D. 38% 65% 34 62 38 54 33 53 33 52 25 50 25 50 36 50 19 50 0 50 100% Current share of women Potential after the general election Nev. Maine Colo. Ore. Md. Calif. N.C. Ill. S.D. 38% 65% 34 62 38 54 33 53 33 52 25 50 25 50 36 50 19 50 0 50 100% Source: New York Times analysis of data from the Center for American Women and Politics at Rutgers University, Associated Press and the National Conference of State Legislatures.

To reach this milestone, however, a woman must win the general election in every district where at least one is running, a difficult feat. Some female candidates are running in districts favoring the other party, and many are challenging incumbents, who historically almost always win.

“The power of incumbency is so, so strong, particularly at the state level,” said Katie Ziegler, a program manager at the National Conference of State Legislatures. “It’s rare for an incumbent to lose their seat.”

Nationally, for women to be at least equally represented as men in all state legislatures, voters in November would need to elect 1,816 more women, nearly doubling the current count of female legislators in state office.

Women now make up a quarter of all state legislature seats in the United States.

Of 7,383 state legislators, 1,876 are women. 1,144 of them are Democrats. 705 are Republicans.

Alaska Alabama Arkansas Arizona California Colorado Connecticut Delaware Florida Georgia Hawaii Iowa Idaho Illinois Indiana Kansas Kentucky Louisiana Massachusetts Maryland Maine Michigan Minnesota Missouri Mississippi Montana North Carolina North Dakota Nebraska New Hampshire New Jersey New Mexico Nevada New York Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Virginia Vermont Washington Wisconsin West Virginia Wyoming

Highest percentages 40%Vermont 40%Arizona 38%Nevada 38%Colorado 37%Washington Lowest percentages 11%Wyoming 14%Oklahoma 15%Louisiana 15%West Virginia 15%Mississippi

“It makes a difference to have women in office,” said Kelly Dittmar, a scholar at the Center for American Women and Politics at Rutgers University. “Women bring different policy priorities to the table,” she said.

But there is a “gender gap in political ambition,” largely because women are less likely to be encouraged to run and more female candidates are likely to doubt their own qualifications, said Jennifer Lawless, the director of the Women & Politics Institute at American University.

While men are often motivated to run by a desire to hold public office, women generally need to be triggered by an urge to “do something,” Dr. Dittmar said. “Something got them angry enough or frustrated enough that they decided they needed to be the person at the table making that decision,” she added.

Women made significant gains in state legislatures in the 1970s and 1980s as more of them entered traditionally male-dominated fields like law, business, higher education and activism — professions that often serve as springboards for political careers.

But in recent years, women’s share of representation has plateaued. Women of color have continued making gains in the last two decades, but they still make up just 6 percent of all state legislatures.

Average percentage of women in state legislatures 50% 25% 22% 8% 0 1975 1999 2018 50% 25% 22% 8% 0 1975 1999 2018 50% 25% 22% 8% 0 1975 1999 2018

Democratic women have made most of the gains. Currently, 37 percent of Democratic state lawmakers are women, compared with only 17 percent of Republicans.

“As long as women’s electoral fortunes are linked to the success of the Democratic Party, it makes it difficult to get past that 25 percent mark,” said Dr. Lawless, referring to the current share of female state legislators. “It makes it linked to how well that side of the aisle is doing.”

The Republican Party “has a very pull-yourself-up-by-your-bootstraps mentality,” so they don’t believe in elevating specific groups, she added.

States with long histories of electing women to office, like Colorado — which first elected three women to its House of Representatives in 1894 — have made the most progress.

Percentage of women in state legislatures across the country Maine Mass. N.H. Vt. Alaska R.I. Conn. N.Y. Mich. Wis. Minn. S.D. N.D. Mont. Wash. N.J. Pa. Ohio Ind. Ill. Iowa Neb. Wyo. Idaho Ore. Del. Md. Va. W.Va. Mo. Kan. Colo. Utah Nev. Calif. N.C. Ky. Tenn. Ark. Okla. N.M. Ariz. S.C. Ga. Ala. Miss. La. Texas Hawaii Fla. State U.S. avg. Above avg. Below avg.

“Women in Colorado take the term limits very seriously,” said Faith Winter, a Colorado legislator who helps run a training program for Democratic women. “So you mentor and bring up the women behind you.”

Representative Faith Winter of Colorado, center, in the State Capitol in March, said her goal was to see at least one qualified woman considered for every open legislative seat. David Zalubowski/Associated Press

Affie Ellis, Wyoming’s first Native American state senator, was motivated to run after visiting the statehouse with her daughter in 2016. At the time, Wyoming’s State Legislature had only one female member.

“My daughter looked into the chamber and asked if they allowed women into the Senate,” said Ms. Ellis, a Republican.

This year, a surge of female candidates has created a larger pool of women advancing to the general election, a sign that more of them could be elected to state legislatures.