A few weeks ago, my wife and I went to a fundraising banquet. We bought 12 raffle tickets, of what I estimate was about 4,000 sold. There were about 30 prizes drawn (tickets pulled randomly from a big bowl), and — to everyone’s surprise — we won four prizes. The prizes were drawn over the course of the evening (ca. 8 draws of 4 prizes each, separated by about 15 minutes), and the bowl was shaken up each time. We didn’t win two prizes in any single draw (so our tickets weren’t “clumped”, as suggested in a comment below).
Question #1: Am I correct that the odds of winning the first prize was roughly 12/3995 (because we didn’t win the very first draw), the second was about 11/3990, the third was about 10/3980, and the last was about 9/3970?
Question #2: To figure out the odds that we’d win four prizes (n.b. nobody else in the room won more than 1!), do I multiply those individual odds?
Question #3: Do the other (ca. 26) draws have to be considered in calculating our odds over the whole evening?