California voters, by a modest margin, think they should be allowed to grow and consume marijuana, according to a new poll that also found more than 1 in 3 voters had tried pot and more than 1 in 10 had lit up in the past year.

The Los Angeles Times/USC poll found that voters back the marijuana legalization measure on the November ballot, 49% to 41%, with 10% uncertain about it. But support for the initiative is unstable, with one-third of the supporters saying they favor it only “somewhat.”

“The good news for proponents is that they are starting off with a decent lead. The good news for the opposition is that initiatives that start off at less than 50% in the polls usually have a hard time,” said Dan Schnur, director of USC’s Jesse M. Unruh Institute of Politics.

The poll also points to a demographic group that is likely to play a key role -- women, particularly those who are married. Men favor legalization, but women are split. Among married women, 49% reject the measure while 40% are in favor of the initiative.

Denise Silva, a 55-year-old court clerk from Pleasanton, in Alameda County, said she is struggling with the issue. “I sway from day to day,” she said. A mother of two grown children, she opposes drug use for moral reasons but knows people who have smoked for four decades with no apparent harm.

“It’s still going to continue to be sold, so since it is, might’s well let the government get their piece of the pie,” she said. Both sides are likely to target mothers, Schnur said. The measure’s backers, for example, could argue that legalization would bring more tax money for schools, while opponents could insist that it would put children at risk.

The poll found voters closely divided on those arguments.

The measure’s supporters say marijuana taxes could raise more than a billion dollars in revenue; opponents dispute that. Among voters, 42% believe that estimate and 38% think it is wildly exaggerated. The November initiative authorizes cities and counties, but not the state, to legalize and tax sales.

In Los Angeles County, the epicenter of the Green Rush with more than 600 medical marijuana dispensaries, voters are most inclined to see pot taxes as a way to plug holes in local and state budgets.

Voters were also split over whether legalized marijuana would worsen social problems, such as increasing crime and triggering higher marijuana use among teenagers. Those concerns appear to have much more potency with voters than the debate over tax revenues. Among those who oppose the initiative, 83% think it would add to the state’s social woes; 55% of married women also believe that.

Raul Martinez, a Democrat from Woodland, outside of Sacramento, said he smoked pot as a teenager. He believes the measure would end up being expensive for local governments. “It’s going to turn around and cost them more money because more crime is going to come from it,” the 47-year-old father said.

The survey of 1,506 registered voters was conducted between May 19 and 26 for The Times and the University of Southern California College of Letters, Arts and Sciences by the Democratic polling firm Greenberg Quinlan Rosner and the Republican firm American Viewpoint. The margin of sampling error was plus or minus 2.6 percentage points for the overall sample and slightly larger for smaller breakdowns.

Attitudes toward legalization diverge sharply by age, with support much higher among younger voters. A 52% majority of voters 65 and older oppose legalization. Among voters between 45 and 64, 49% support it. But among those 30 to 44, 53% are in favor, and that rises to 61% among those 18 to 29.

Chris Donnelly, a 25-year-old substitute teacher from San Diego, has never touched pot but strongly favors the initiative and believes it could support schools. “It wouldn’t bother me one bit if marijuana were legal,” the unaffiliated voter said. “I don’t think it’s any more harmful than alcohol.”

The poll also offers an unusually detailed look at who is using marijuana in California.

Among those surveyed, 37% of voters said they had tried pot -- a figure roughly consistent with federal surveys of drug use -- and that group strongly supports the initiative. The 11% who had used marijuana in the last year favored legalization by a landslide, 82%.

By contrast, the 57% of voters who said they have never used marijuana oppose the initiative.

Though certain types of voters are more likely to light up, marijuana use cuts across all demographic slices, reaching beyond the cliches of skateboarders and aging hippies.

A matchup in the governor’s race between Democrat Jerry Brown, who governed the state in the 1970s, and Republican Meg Whitman, the former EBay executive, clearly illustrates this. Voters who have tried marijuana make up 45% of Brown’s supporters, and 37% of Whitman’s. But both candidates oppose legalization.

Among Democrats and voters who decline to state a party affiliation, 12% had used marijuana in the last year, as had 7% of Republicans. About a quarter of the voters in each slice of the state’s electorate said they experimented with the drug in the past, but not in the last year.

One of the biggest differences is between men and women. Among male voters, 45% said they had used marijuana, 14% in the past year. Among female voters, 29% said they had tried it, but just 8% in the past year.

The heaviest use of marijuana skipped a generation. The youngest voters, between 18 and 29, reported the highest percentage of marijuana use in the past year, followed by voters between 45 and 64, who could be their parents or even grandparents. Most of those voters came of age in the marijuana-hazed Vietnam War era.

The chance that a California voter has used marijuana is higher for college graduates than high school graduates and rises with income. Use is highest among single voters and lowest among married ones. Voters north of the Bay Area, home to the weed-raising Emerald Triangle, are most likely to have used marijuana, while voters in the Central Valley are least likely.

john.hoeffel@latimes.com