Cycling probability question

I recently saw on a website promoting cycling as a safe activity the following statement: "The Cyclist's Touring Club has about 60,000 members. On average, there are about 3 to 5 member fatalities per year. That means, if the average CTC member rides 15,000 years, he'll reach a 50% chance of a fatal bike accident."

This bothered me. I accept that there is a fatal accident on average every 15,000 years of individual cycling, but the 50% chance seemed to be plucked from thin air.

It seems to me the way to work out the correct probability is similar to how you work out the probably of hitting at least one card of a particular suit from 4 random cards in a deck.. which is as I understand it, you take the probability of NOT hitting your suit for each card (.75) multiply them together and subtract the answer from 1. So, 1 - (.75 to the power of 4) comes to about .68.

Seems to me the calculation for the cycling problem would be: 1 - ((14,999/15,000) to the 15,000th power) = .6321...

(14,999/15,000 I believe would be the chance of a member NOT having a fatal accident for one single year).

Am I correct? ..and I'm just curious, does anyone know if this number .6321 etc occurs elsewhere in mathematics, statistics.. nature?? It seems to me that all probably problems of this type settle on a number like this.

Airline passenger fatalities are often expressed in relationship to miles flown but the real risk is usually at take off and landing, so total miles flown means very little.
Cyclists are probably at greater risk in heavy traffic so those are the miles that count.
Cyclists riding in groups are probably more visible and cyclists on trips often have a sweep van with a sign warning "cyclists ahead".
So miles may be a misleading statistic.
And fatal accidents may not relate to actual safety if many victims are persistently vegetative but not dead.

Quote: rocket226

Seems to me the calculation for the cycling problem would be: 1 - ((14,999/15,000) to the 15,000th power) = .6321...

(14,999/15,000 I believe would be the chance of a member NOT having a fatal accident for one single year).

Am I correct? ..and I'm just curious, does anyone know if this number .6321 etc occurs elsewhere in mathematics, statistics.. nature?? It seems to me that all probably problems of this type settle on a number like this.

Yes, and 0.6321 is 1 - 1/e where e = 2.71828459045...

e is very important in math. It is part of the result if you continually compounded interest. And in calculus, the integral and derivative of e^x is still e^x.

http://en.wikipedia.org/wiki/E_(mathematical_constant)

Thanks for your answers.. Interesting about the constant e. I hadn't come across that before. Guess they didn't teach us that one in school.
Nice to know I was right too! I think I will point out the error to the website owners.