We throw 250 darts (one by one) at 1200 dart boards. Each dart strikes a board randomly. No dart's strike affects any other. What is the probability that two darts will strike the same board?
I make it 1 in 1200, b/c the probability of the 1st dart striking a board is 1. The probability of the 2nd dart striking the SAME board is 1/1200. Correct?
2nd part: When all 250 darts have been thrown, what is the probability that ANY two have struck the same board? Using the same reasoning: the first dart strikes one board out of 1200, the second 1 board out of 1 occupied and 1199 unoccupied (1:1199), 3rd 1 board out of 2 occupied/1198 unoccupied (2:1198), etc. This is not a factorial b/c we don't care which boards are hit -- they aren't unique. When 249 have been thrown, the odds that #250 will hit an occupied board are 249:951, or less than 25%. Correct?