@Ashwin_s is this a parody? The two math problems are not equivalent. If you don’t see this, perhaps we need to start with the basics of probabilistic analysis and combinatorics. You seem to falling prey to the gamblers fallacy and the birthday paradox at the same time!
These are cases where simulation could really help you, especially because you are a programmer. I suggest you stop arguing semantically and start understanding the math.
Exactly.