$10M in US $100 bills would take up over 100 liters of volume, which would fill about five rather large briefcases. The cash itself would weigh over 200 pounds. Strictly speaking, it's impossible for someone to walk up to you on the street and simply "hand" you a briefcase full of $10M. They would have to wheel them to you on a cart, which would undoubtedly attract far more attention than is safe for this sort of transaction.

Incidentally, it's amusing to note that $100 bills are actually more valuable than gold relative to their weight. The obvious next question would be, what's an even denser store of value. For one amusing example, Cristiano Ronaldo has a transfer value in excess of $130 million by last valuation, and weighs less than 200 pounds, making him more than ten times as valuable as $100 bills per unit weight, let alone gold. Judging from the transfer market, it would seem that many top-flight athletes are literally worth their weight in gold.

>It's not out of the realm of probability.

It's entirely out of the realm of probability, although just slightly within that of possibility.

You're assuming that there is actually someone walking around out there with a briefcase full of $10M that he or she intends to give to someone. At least with the lottery you know that someone is actually getting a lot of money.