(CBS) -- Fifty years after the March on Washington, there is a wide divergence between the views of white and black Americans on the issue of racial discrimination. While sizeable majorities of both whites and blacks think there is at least some racial discrimination today, blacks are more apt to say it is widespread. Forty percent of blacks say there is a lot of discrimination against African-Americans today, compared to just 15 percent of whites who say that.
Differing views may be a result of different personal experiences. Just 29 percent of whites say they can think of a specific instance where they felt discriminated against because of their race, but this rises to 62 percent among blacks.
Race Relations Today
At the same time, more than half of Americans - 57 percent - think race relations in the United States are generally good. This is down slightly from early last year, and nine points lower than the high of 66 percent reached in April 2009, shortly after President Barack Obama took office. A third says race relations are generally bad.
Views of race relations may be a bit less positive today compared to recent years, but they are considerably more upbeat than they were in the 1990s. In 1992, amid the riots in Los Angeles, just 25 percent of Americans described race relations in the country as generally good.
There is a racial divide on this question as well, with white Americans more optimistic about race relations in the U.S. than blacks. Fifty-eight percent of whites believe race relations are good, but among African-Americans, opinion is more divided: 46 percent think race relations are good, but almost as many - 41 percent- say they are bad. The percentage of African-Americans who say race relations are generally good has dropped nine points since January 2012.
As has historically been the case, Americans rate race relations in their own community more positively than race relations in the country overall. This is true among both white and black Americans. Seventy-nine percent of Americans say race relations in their own community are generally good while 57 percent say they're generally good in the U.S. overall.
Perhaps one of the most striking indications of the changing perception of race relations comes from Americans' shifting attitudes about interracial marriage. Today more than eight in 10 Americans (82 percent) approve of marriage between blacks and whites, including large majorities of both black (88 percent) and white (82 percent) Americans.
Even in the South - where laws against interracial marriage stayed on the books in every state in the region until they were deemed unconstitutional in 1967 - three in four Americans (74 percent) approve of marriage between whites and blacks.
Approval of marriage between blacks and whites has risen dramatically over the years. According to Gallup polling, 73 percent of Americans approved of marriage between blacks and whites 10 years ago, and just 48 percent approved back in 1994. As late as 1983, more Americans disapproved (50 percent) than approved (43 percent). When Gallup first asked Americans whether they approved or disapproved of marriage between "white and colored people" back in 1958, just 4 percent of Americans approved.
This poll was conducted by telephone from August 7-11, 2013 among 1,006 adults nationwide. Data collection was conducted on behalf of CBS News by Social Science Research Solutions of Media, PA. Phone numbers were dialed from samples of both standard land-line and cell phones. The error due to sampling for results based on the entire sample could be plus or minus three percentage points. The error for subgroups may be higher. Interviews were conducted in English and Spanish. This poll release conforms to the Standards of Disclosure of the National Council on Public Polls.