Do you not see, though, how comprehensively this invalidates your entire line of argument? If there are 140,000,000 tickets in a lottery, and you happen to buy ticket no. 27,598,163, that's a 1 in 140,000,000 chance, bit every other ticket is just as unlikely to have been the one you bought. If it's equally unlikely that "now" falls within any specific 100 year period, then it's equally unremarkable that "now" falls within any 100 year period. Your argument therefore equates to the argument that it's impossible to buy a lottery ticket, a conclusion you can invalidate trivially simply. It is, in fact, as practically everybody has been repeatedly pointing out to you, in our role as teachers to yours as the inattentive and demotivated student, an exact statement of the Texas Sharpshooter fallacy.
Dave