ChrisHallquist comments on Yes, Virginia, You Can Be 99.99% (Or More!) Certain That 53 Is Prime - Less Wrong
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I am not entirely sure about this, since I have made a similar mistake in the past, but If I am applying my relatively recent learning of this correctly, I think technically it suggests that if 1 million random people drive 100 miles, one of them will probably die, and based on a quick check of top causes of car accidents, we would also expect that person to be at least one of: Distracted, Speeding, Drunk, Reckless, in the Rain, Drowsy etc...
And if you are currently an undistracted, alert, sober driver who is following all traffic rules in dry weather, your chances of an accident during this particular drive are notably lower (Although I don't know if they are low enough for driving to be safer then a plane because I don't have sufficient statistics on that.)
Edit: Actually I think I'm still insufficiently clear. Technically, we wouldn't be able to expect that they had at least one risk factor without knowing the overall prevalence of those risk factors in the overall population. Admittedly, I did include 'Speeding' as a risk factor and my understanding is that speeding is quite common, (and I did include an etc. to include other non listed risk factors, which would also increase the chance of at least one of them being true) but I haven't actually run the numbers on my expectation above either.
This fits with what I've read, though I'd point out that while we get our share of anti-drunk driving and now anti-texting-while-driving messages, most people don't seem to think driving in the rain, driving when they're a bit tired, or being a bit over the speed limit are particularly dangerous activities.
(Also, even if you're an exceptionally careful driver, you can still be killed by someone else's carelessness.)
I don't think most people believe that driving when they're very tired is especially dangerous.