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.
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%.
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.
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.
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.
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.
Also, one other note - I was talking about riding experience, not absolute age - something the CDC doesn't track, but other large studies I've seen do. There's a strong correlation between experience - whether gauged by years of riding or, even better, raw mileage.
There's also a huge correlation between unlicensed riders and serious injuries. Motorcycle riders are far more likely to be unlicensed than car drivers - last I heard was something like 3-4 times as likely.
Unlicensed motorcycle riders are over twice as likely to be in fatal accidents than licensed motorcycle riders.
I ride 15,000-20,000 miles a year - I'm well trained, equipped, and experienced. A lot of bike owners ride weekends, occasional trips, etc. I actually don't ride much on the weekends - and when I do, I'm pretty shocked how bad (dangerous, rude, etc) the riders are compared to the commuters I mostly see.
