# Probability - what is the probability that a given tire length will lie in a lenght of interest

Walking across a street and lookign at tires I've had a thought. If a car is rolling on a road starting at point O, at each time some area of a tire is touching the road, what if after some random distance L there are 2 points - A and B, the distance from A to B is 100cm.
A tire of that car has a length of 1000cm, of that 1000cm, 10cm is painted red - R.

What would be the probablity that all of the painted area R would be inside points A and B. The area R would need to lie fully inside A & B, it can't start in outside of AB and end in AB or start in AB and end outside of AB - only in between AB.

How the probability expression would change if instead of random distance L we would assign a distance from point O to A. My first thought is that it would not change as there is another random factor - what is the starting position of a tire ( where the area R is from the starting point O ).

I've added an image drawing this question for easier visualization.

• Schwartstack