## Just Answer 1/e Whenever Anyone Asks This Kind Of Question

I recently had the chance to ride the Leap-the-Dips at Lakemont Park (Altoona, Pennsylvania), the world’s oldest operating roller coaster. The statistics of this 1902-vintage roller coaster might not sound impressive, as it has a maximum height of about forty feet and a greatest drop of about nine feet, but it gets rather more exciting when you consider that the roller coaster car hasn’t got any seat belts or lap bar or other restraints (just a bar you can grab onto if you so choose), and that the ride was built before the invention of upstop wheels, the wheels that actually go underneath the track and keep roller coaster cars from jumping off. At each of the dips, yes, the car does jump up and off the track, and the car just keeps accelerating the whole ride. (Side boards ensure that once the car jumps off the tracks it falls back into place.) It’s worth the visit.

Looking at the wonderful mesh of wood that makes up a classic roller coaster like this inspired the question: could any of it be original? What’s the chance that *any* board in it has lasted the hundred-plus years of the roller coaster’s life (including a twelve-year stretch when the ride was not running, a state which usually means routine maintenance is being skipped and which just *destroys* amusement park rides)? Taking some reasonable guesses about the replacement rate per year, and a quite unreasonable guess about replacement procedure, I worked out my guess, given in the subject line above, and I figure to come back and explain where that all came from.

## BunnyHugger 5:36 pm

onSunday, 4 August, 2013 Permalink |I’m delighted that this could manage to be the source of one of your math puzzles just as I use it for one of my philosophy puzzles for class.

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## Joseph Nebus 3:49 am

onMonday, 5 August, 2013 Permalink |Yeah, I’m glad it offers meaningful problems in both our fields.

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## Why I Say 1/e About This Roller Coaster | nebusresearch 5:09 pm

onTuesday, 6 August, 2013 Permalink |[…] Just Answer 1/e Whenever Anyone Asks This Kind Of Question […]

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## Why I Don’t Believe It’s 1/e | nebusresearch 5:26 pm

onFriday, 9 August, 2013 Permalink |[…] of answers why despite my neat reasoning and mental calculations I don’t really believe that there’s a chance of something like one in three that any particular board from the roller coas… is still in place. The picture — from the end of the track, if I’m not mistaken — […]

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## My August 2013 Statistics | nebusresearch 2:31 pm

onSunday, 1 September, 2013 Permalink |[…] Just Answer 1/e Whenever Anyone Asks This Kind Of Question (part of the thread on the chance of the 1902-built Leap-the-Dips roller coaster having any of its original boards remaining) […]

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## Roller Coaster Immortality Update! | nebusresearch 7:12 pm

onFriday, 17 April, 2015 Permalink |[…] I wondered whether any boards in it might date from the original construction in 1902 by the E Joy M… If we make some assumptions we can turn this into a probability problem. It’s a problem of a type that always seems to be answered 1/e. (The problem is “what is the probability that any particular piece of wood has lasted 100 years, if a piece of wood has a one percent chance of needing replacement every year?”) That’s a probability of about 37 percent. But I doubted this answer meant anything. My skepticism came from wondering why every piece of wood should be equally likely to survive every year. Different pieces serve different structural roles, and will be exposed to the elements differently. How can I be sure that the probability one piece needs replacement is independent of the probability some other piece needs replacement? But if they’re not independent then my calculation doesn’t give a relevant answer. […]

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