Found a probability problem on twitter and found the solution to be counterintuitive:
At 1 minute to midnight, 10 apples fall into a sack. The same happens at half a minute to midnight, then at a quarter minute to midnight, and so on. At each such event you remove an apple randomly from the ones still present in the sack.
What is the probability that at midnight strike the sack will be empty?
For the first iteration of apples: 10 falls, 1 gets immediately removed leaving 9 in the bag.
Second iteration of apples: 10 falls, 1 gets immediately removed leaving 19 in the bag.
The bag appears to approach infinitely larger size, so it would never be empty.
What am I thinking about incorrectly?