Probability and Traffic Flow
Imagine you're a city planner in charge of building new roads in Chaosville. You and your team have decided that you need to add roads between a new neighborhood and three sections of town. The current roads are just gravel and haven't been paved yet. This year the town has decided it is time to pave the roads, and your job is to decide how wide each road should be. There are three roads and there is only enough money to make one of them four lanes. The other two will have to be two lane roads. Your mission, should you choose to accept it, is to determine which road should have four lanes.
Basically, the roads look like this on the map:
After going out and watching the traffic for a few mornings, you make a startling discovery. At each fork in the road, about half of the cars turn left, and the other half turn right. You and your team have a Chaos set in your office and have decided that it could be useful in making a model of the situation. The track can represent the road, and pendulum switches can determine which way the cars turn. The cars will be the balls rolling down the track.
Build the following setup. You should have two forks in your road, with a pendulum switch at each one. Be careful to line up the pendulum switch directly below the ball drop.
Stage 1: The Traffic Experiment
It's time to run a traffic experiment. We can roll balls down the track and see how many balls go on each track. These balls represent the number of cars that go down each of these roads in Chaosville. Roll thirty balls and count how many go to each section of town. Which road do you think should have four lanes? Why?
Refer to the map of the roads in Chaosville. If exactly half of the cars go each way at each fork in the road. After 40 cars have driven down the road, how many will have taken each exit?
Answer: 20 at exit 1, 10 at exit 2, and 10 at exit 3.