My family took a lot of road trips when I grew up. To combat boredom, we tried to see how many state license plates we would see on our trip. On a trip to see Mount Rushmore, we found almost all of the states.
As an adult and geek, the license plate game has (subtlety?) changed. Now, I combat boredom by talking with my husband about how to come up with a probability distribution for how many state license plates we would expect to see on a road trip from point A to point B.
We took two road trips this year: one from Richmond, VA to Chicago, IL over the summer, the second from Richmond, VA to Burlington, VT over the winter break. We saw ~35 states in our first trip and ~25 states in our second trip. My husband and I immediately noticed that we accrued license plates at a slower rate on our winter trip, which we suspect was from fewer people making road trips over the winter as compared to summer.
We wondered if one could estimate how many license plates you would expect to see in a road trip based on
- the states you drive through,
- the time of year (more people take road trips in the summer)
The state that you are in determines how likely you are to see other state license plates based on their relative distances as well as the number of licensed drivers in other states.
We simplified the problem to avoid looking at how long you drove through a state as well as interstate connectivity issues. That is, there is no difference between driving through West Virginia on I-70 and driving through Pennsylvania on I-80. Additionally, if you are in I-80 in Illinois, you are connected to neighbor states Iowa and Indiana but not neighbor states Missouri and Wisconsin, and therefore, one might expect to see Iowa and Indiana plates. We ignored this and just noted that you would be in Illinois, which gives the likelihood of seeing license plates from other states regardless of “route distance.”
My next post summarizes the model, the assumptions, and the results.
Have you tallied license plates on road trips? What do you think are the salient aspects of this problem to include in a probability model?
Punk Rock Operations Research 
January 19th, 2012 at 10:19 am
I have a strong memory of being a kid on our yearly Ohio-Winnipeg trip (took 2 weeks dragging a trailer around). At one campground, there was a car with Alaska license plates! I think every kid within five miles was there, checking off that hard-to-find state.
January 19th, 2012 at 1:00 pm
@miketrick, We saw Alaska on both of our recent trips. (Lightning struck twice!)
January 27th, 2012 at 7:03 pm
Interesting post again. Laura! I lived in Ohio and Pennsylvania as a kid and Alaska and Hawaii plates were tough to find, but the hardest one for me to find was Utah.
I guess all those Mormon missionaries took the bus back then, or something. I decided that Utahns must have stayed home more than anyone back in those days or at least didn’t drive on long trips.
February 7th, 2012 at 2:38 pm
[…] is estimating probability of outcomes. That’s why I think Prof. MacLay’s posts about the license plate game are pretty neat. It’s a great example of how to estimate probability based on observation, […]