The Matching Car

1. To pass the time while driving, you start looking for cars with the same three-digit number on their license plates as you have on your own. Assuming three-digit numbers are uniformly distributed among the cars you'll be passing, what is the average number of cars you'll pass before you'll see a matching car?
2. Now tired of that game, you exercise your memory - what is the average number of cars you'll pass before you'll see a duplicated three-digit number?

Source: Reader Rich Polster.