[lutusp]

> Someone mentioned it being akin to motorcycling riding, but I can't imagine that 2% of motorcyclists die from it.

The rates for motorcycle accidents and deaths is really very high:

http://en.wikipedia.org/wiki/Motorcycle_safety#Accident_rate...

Quote: "According to the U.S. National Highway Traffic Safety Administration (NHTSA), in 2006, 13.10 cars out of 100,000 ended up in fatal crashes. The rate for motorcycles is 72.34 per 100,000 registered motorcycles."

That's about 5 1/2 times greater.

[johnny99]

That's on a per-vehicle basis. On a per-mile basis they're dramatically more dangerous: per mile travelled, motorcyclists are 37 times more likely to die in a crash than passenger car occupants:

http://www.aaos.org/news/aaosnow/jul12/clinical1.asp

I gave up my brief motorcycle career after having kids, which I'm rather glad of now, reading that.

[Tossrock]

And still much less than 2%.

[Retric]

72.34 per year per 100,000 registered motorcycles * 30 years is 2.17%.

Worse plenty of people own more than one motorcycle so the rate is probably higher than that.

[jedmeyers]

Those are not the same "motorcycles" each year, so you cannot multiply by 30.

[vilhelm_s]

How do you mean? The suggested calculation is: In any given year, a motorcycle owner has a 72/100000 chance of dying. So if you own a motorcycle for 30 years, the chance of dying is approximately 30*72/100000.

[Tossrock]

That is not how a binomial probability is calculated. Consider the case where you flip a coin twice - do you have a 2 * 1/2, or 100% chance of getting a 'head'? Obviously not – you have a 75% chance.

The actual way you calculate the probability of an event with a binomial distribution is by taking the inverse probability and raising it to the power of the attempts, then subtracting from 1. So in the case of two coin flips, that is 1 - (1/2 ^ 2), or a 75% of getting a 'head'. That would mean, with a huge host of assumptions, that a motorcyclist's chance of dying over 30 years would be 1 - (99928/100000)^30, or (funnily enough), 2.13%.

edit: I said bimodal when I meant binomial.

[vilhelm_s]

That's why I said "approximately". :)

By the binomial series [1], the true value is 1-(1-p)^n = np - n(n-1)/2! p^2 + n(n-1)(n-2)/3! p^3 + ...

So approximating it to just np corresponds to taking just the leading term of the series. Of course, this is only valid when p is small enough. To see how good the approximation is, we can compare it to the two first terms of the series, which is np - n(n-1)/2 p^2, or approximately np - (np)^2 /2.

So the approximation np is about twice the percentage difference between the approximation and the true value. In this case, the approximation np is about 2%, and that guess is itself about 1% wrong.

[1] https://en.wikipedia.org/wiki/Binomial_series

[lutusp]

You certainly deserve my upvote. :)

You set out to correct a naive statistical assumption, computed it properly, and the result was about the same (not at all common for such problems). But you posted it anyway, in the spirit of sharing useful information.

As the Australians say, "Good on you, mate."

[rogerhoward]

If you own a motorcycle for 30 years, your chances are not the same every year - your chances of dying on a bike are higher when you're younger and when you have less years on a bike. So every year I ride, my chance of dying that year on a bike gets smaller.

In other words, the bulk of deaths on bikes are young, inexperienced, and/or unlicensed riders.

Also, bike deaths are far more likely to involve alcohol than car deaths; so if you're like me and you don't drink before riding, you've just improved your chances.

[Retric]

Not really, your odds do change as a non drinker but age is far less important than you might think. Your hypotetical driver that owns a motorcycle for 30 years is more likely to die over 25 than under it.

http://www.cdc.gov/features/dsMotorcycleSafety/

A significant reason for this is your far less likely to survive an accident as an older rider than a young one.

Note: The death rate statistics they quote include non motorcycle owners.