The Wave: Hiking, Dogs, and the Binomial Probability Equation
Meet Your Guide
Hi! I’m Maureen, Cultivate’s Measurement and Analytics Lead. To introduce myself, I’m going to tell you a bit about hiking, my dogs, and the binomial probability equation. Strange, I know - but I promise that it will give you a little glimpse into the way that I see the world, my passions, and how I approach problems.
I traveled from my home in Maine to Utah with my two dogs, Tulah and Zorro, for the month of January. I specifically planned to stay in the lovely town of Kanab which is the home of Best Friends Animal Sanctuary (the country’s largest no-kill animal shelter) and claims to have the “Best Earth on Show” (I agree).
Kanab is also the host of the lottery to obtain a permit to hike Coyote Buttes North. The area is the home of The Wave – a multi-colored rock formation created by millions of years of erosion of the Navajo Sandstone that forms the Paria Canyon-Vermillion Cliffs Wilderness. Or, you may recognize it as a screensaver from Windows 7.
Photo by William H. Belvin
The Wave
Each day there is a lottery to win one of 4 permits to hike the Wave (to be specific, it’s 4 groups or 16 people, whichever comes first). Since I’ve been here in the off-season, the number of hopeful groups each day has ranged from 14 to about 60 – during the peak season it can be much more!
I’m going to simplify this a bit, but on average, I’ve had about a 15% chance each day to win a permit. I have been to the lottery 28 times. I STILL haven’t won. What gives? What are the chances I would be this unlucky?
Let’s put it this way, if this scenario played out 100 times in a simulation, in essentially only 1 of them (1.05 to be exact) would I still be waiting for my chance to hike The Wave. In fact, it’s more likely that I would have been called multiple times than to not have been called at all. Oof.
So how do I know this? In my former life, I taught university-level statistics. The binomial probability formula is used to calculate probabilities in this type of scenario.
The Math
If you want to know the probability of x successes (0 for me so far!!) in n trials (28 times waiting for my number to be pulled) with p being the probability of success (.15) and q the probability of failure (.85) on each trial you can use this formula to find out the chances of being an unlucky hiker, like me. And yup, it’s about 1%.
Even though I haven’t had a chance to hike The Wave, I’ve sought out all the amazing opportunities Southern Utah has to offer. Each day I haven’t gotten a permit has provided me the opportunity to dive a little deeper into my research about the area and find new trails, hikes, and vistas to explore.
Beyond the Wave
Given my luck, you may not want to travel to Las Vegas with me. But, you can be sure that I’ll always take a data-driven, curious, and scientific approach to problems. And, I’ll do it while exploring and making the most of my situation with the best traveling buddies you could ask for. Maybe I’m not so unlucky after all!
Left + Right photos by Maureen Gillespie. Middle photo by Matthew C. Doherty
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