While I agree with you in philosophy, I wonder if that is the best example. I don't think I've ever seen a news report of someone getting hit by lightning and a bus at the same time, but people do seem to win the lottery on a fairly regular basis. This suggests that winning the lottery may be the more likely of the two.
If it was a tax on the poor and undereducated, the correlation should be negative, yet the first three articles I found on the matter said it's positive, and that income is the strongest determinant of gambling activity.
Secondly simply looking at the number of times person partakes in an activity or just how much they spend only gives a small and incomplete picture. The really important number is what proportion of their total income is spent on gambling. Most studies seem to find that the poor spend a higher proportion of their income on lottery tickets than richer people.
A couple of randomly chosen references: http://walkerd.people.cofc.edu/360/AcademicArticles/LotteryR... http://www.cfcg.org/articles/CPGI_report-Dec4.pdf