Dave Wins the Powerball! And Quits Writing Sentences!

Actually, not quite . . . April Fools . . . neither you nor I are quite so lucky-- I will continue to write this drivel (and I hope you will continue to read it) because I did NOT win the Powerball (and it's not like I'm doing this for the money, anyway, so even if I did win the Powerball, I would continue writing this thing, because the Dalai Lama told me there will be no money, but on my deathbed, I will receive total consciousness . . . so I've got that going for me) but something very, very statistically unlikely happened and I had the perspicacity to notice and the mathematical acumen to figure out just how unlikely this event was . . . I teach Creative Writing, which is an elective that is open to sophomores, juniors, and seniors and I usually have an equal mix of the three grades in each class-- no particular grade is favored, but this year I have a thirty person class which contain zero juniors, and the chance of this happening is highly unlikely . . . there is a 66% chance for a class of one person to have zero juniors in it, and a 43% chance for a class of two to have no juniors in it (2/3 multiplied by 2/3) and a 29% chance that a class of three has no juniors in it, and if you continue in this fashion for a class of thirty, you have to calculate 2/3 to the 30th power, which comes out to 0.0000038576077564 (that's a 1 in 259,228 chance . . . which is pretty tiny, statistically speaking, but not quite as small as your chance of winning the Powerball lottery, which is 0.0000000057142857 or a 1 in 175,000,000 chance) and I'm wondering if there is some other explanation . . . perhaps junior schedules this year somehow prohibit them from taking electives period 7/8 . . . or maybe I should run out and buy a lottery ticket and strike while the iron is hot.