The probability of Asian-Hispanic food

From tomorrow's New York Times: an article on the growing prevalence of Asian-Hispanic fusion food in California. It's part of a series on the Census. Orange County, California is 17.87% Asian and 34.13% Hispanic -- so the majority of the population, 52.00%, is either Asian or Hispanic. Not surprisingly there's a guy there with a food truck named Dos Chinos, which serves such food as sriracha-tapatito-tamarind cheesecake.

This is accompanied by a little map showing the sum of Asian and Hispanic population in any given county. (Well, it might be the sum; to be honest I don't know, as in the Census "Hispanic" vs. "non-Hispanic" is orthogonal to "race", which takes values White, Black, Asian, American Indian, and Native Hawaiian.) In many places in the southern half of the state it's over 50%.

But wouldn't the relevant statistic for this article be not (0.1787) + (0.3413), but 2*(0.1787)*(0.3413) = 0.1219, the probability that if two random Orange Country residents run into each other, one of them will be Asian and the other will be Hispanic? Fresno County, for example, is 50.3% Hispanic and 9.6% Asian -- that's 59.9% "Hispanic or Asian" -- but there wouldn't seem to be quite as many opportunities for such fusion as the probability of a Hispanic-Asian pair in Fresno County is only 2*(50.3%)*(9.6%) = 9.7%.

(Except that 97% of Fresno County's Asians are Hispanic, according to the frustratingly hard-to-navigate American FactFinder.So maybe some "fusion" has already taken place.)