So, this is a freshman probability problem and I am embarrassed to p[ost it, but I have been up for 35 hours and my brain is broken.
I have an urn with 60,000 white balls and 6 red balls. From this urn I make 60,000 draws with replacement. What is the probability that I draw no red balls?
Doing this numerically, first with a spreadsheet and then with R, I keep getting 0.00248, roughly.
((1- 6/60,000)^60,000) I expected it to be small, but that seems too small, intuitively, Also, the number is suspiciously close to e/1000, which kind-of fits, I think, raising a really low probability to a really high power. But the answer is on the order of 100 times smaller than I expect, based on just gut feeling.
Just for human interest, this number should be roughly the probability that the Current Population Survey sampled no one with incomes above $2 million in 2011, as indeed it didn’t. And assuming (falsely) that rich people are as likely to answer as anyone else.