Answer TRUE or FALSE.
A company wants to use a system where they randomly assign each customer a 9-digit ID (so there are 1 billion possible ID numbers). Of course, there is a chance that two customers will be assigned the same ID. But the company figures that risk is OK if the odds are small enough. They expect to assign IDs to 1000 customers. The chance of a collision is therefore one in a million.
While it is true that the last customer given an ID has about one chance in a million of sharing it with another customer (actually, the chance is 999/1,000,000,000 if 999 IDs are already assigned)...
... this logic does not account for the fact that any of the previous 998 assignments might also have caused a collision.
So the chance for a collision is rather higher than one in a million.