Expected Number of Cars in a Parking Space

Question

Another expectation problem:

There is a parking space of length 4. Cars come and randomly choose any
position to park over the interval [0, 4]. Each car occupies a space of
length 1. Calculate expected number of cars that can park.

I am trying to solve it using indicator random variables, but I am not able to form any (probably because the parking lane is not discrete....??). I am confused here. Can I have some hint over here please ?

Answer 1

Hint: draw a square, with $x$ being the center of the first car and $y$ the center of the second car. We must have $0.5 \le x,y \le 3.5, |x - y| \ge 1$, so shade the part of the square that is allowable. Now what fraction of that area can accommodate another car? As you will always fit two cars and never fit four cars, all you care about is whether the third car fits.

Answer 2

Hint:

What is the probability that four cars could park? Try some arrangements for three cars, what is the probability that three cars could park in one of these arrangements? Are there any arrangements such that only two cars could park?