(Submitted by Skepticality listener James Garrison)

A few years ago, I began working for OKC Animal Welfare. The day I was released to work in the kennels, I was helping a citizen look for her dog, and was trying to explain the process.

The shelter has 5 rooms for dogs, divided by age, size, if they’re adoptable or not, and if they’re involved in a case. I took her into the first room, which was normally reserved for dogs under 6 months, and I pulled the first cage card we came to and explained what she needed to do if she found her dog.

As I put the card back, she looked into the kennel, looked at me and said “That’s my dog!”, which turned out to be an older border collie looking dog, so it shouldn’t have been in that room in the first place, and it’s stray time was up. (Luckily, they were going to try and place it in the adoption program, otherwise she would never have found it.)

At the time, in 2007, the shelter took in around 35 to 38,000 animals a year (roughly half of them dogs), the shelter probably held around 200-300 dogs that day (that’s the general average) and the human population of Oklahoma City was 546,000.

As well, a large percent of the dogs in the shelter never made it to adoption due to various factors, including temperament, health, and space. Another consideration is that probably only 10% of loose dogs are reported or come into the shelter.

Given that roughly 100-300 people came into the shelter a day, and they get nearly as many animals a day, what are the odds of finding a specific person’s dog in the first kennel on my first day in the shelter?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 265.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society, and watch her on Virtual Skeptics.

Only a few pieces of information are needed to estimate the odds the way the author framed the question, but the author does not provide the most important: the odds that a specific dog would end up in the shelter. However, let’s pretend that the 10% mentioned answers that question. If there is a 1 in 10 chance that a dog would end up in the shelter, then there is a 1 in 10 chance that any given visitor’s dog will be found there. We must assume that if the dog is at the shelter, the owner will find it. It’s just a matter of when. Since there are 5 kennels, then we can multiply that probability by 1/5th to find the probability that a person’s dog will be found in the first kennel. That makes it .02 or 1 in 50 that the owner will find their dog and find it in the first kennel. In other words, as the question is framed, the odds are not crazy at all.

The number of people visiting the shelter and the number of dogs housed in it are irrelevant. No owner would just sample the dogs; they would want to do an exhaustive search of the shelter to find their dog. Likewise, the population of the town is irrelevant.