The National Journal says: “The odds of being killed by a shark are about 1 in 3.7 million. The odds of being killed by a sting from a bee, wasp, or hornet are 1 in 79,842, according to the National Center for Health Statistics, a part of the Centers for Disease Control and Prevention.”
Now you see these kinds of stories all the time, all of which have conclusions like You have a better chance of dying in a lightning strike than in winning the lottery, etc., etc.
These stories are all wet. Nobody has a chance of dying in a lightning strike, just as nobody has a chance of winning the lottery or being killed by stinging sharks or biting wasps. By which I mean, everybody has a chance of winning the lottery or being stung by lightning or whatever.
Double talk? The problem is chance, a nebulous word, apt to change shape mid-sentence so that you don’t always end up where you were aiming.
In one version, chance means logical possibility. Everybody has the logical possibility of dying by shark, bee, or lightning. But chance also connotes probability. And there just is no unconditional probability of dying by anything.
Logical possibility is a weak criterion. Anything that isn’t logically impossible, such as square circles, is logically possible. You might be a native Antarctican, solid ice your bed and fluffy snow your pillow since birth. But, one day, an evil Polar Vortex might surreptitiously search the seas for your doom, and fling a hammerhead shark from the tropics to the very spot on which you take your morning ice floe stroll, as was illustrated in the documentary Sharknado.
Hey, it could happen. It’s logically possible. And in that sense you have a chance of dying by shark bite.
But you don’t have an unconditional probability of dying by one. What can we say? If the probability of you being eaten by a shark were 0, then it would be impossible, logically impossible, that you could be eaten by a shark. But we’ve already agreed that it is logically possible. And if your probability is 1, then that means the universe guarantees, no matter what, you will have your head bit off. Ouch.
This means the probability of you dying by shark bite, without knowing anything else about you (and I mean this clause just as it’s written), is no number at all, but all numbers between 0 and 1. Which is fairly useless, as far as information goes, But not entirely unless since non-extreme probability tells us a event is contingent, i.e. logically possible.
We can now see that it makes no sense to say the unconditional probability of dying by a bee sting is “larger” than of suffering the consequences of a sharknado. These probabilities, in the absence of any other information, are equal.
What “other information”? Example: your aunt Narantsetseg lives in central Mongolia, far from the sea and inland aquariums, whilst you live in Key Largo in a beach shack. Given only this information, which includes common knowledge about these locations and their nearness to sharks, it’s natural to say you have a larger probability of dying of shark bite than your aunt.
How much larger? We don’t know. There’s still not enough information to quantify the difference. Why? All probability is conditional on the information supplied. If that information is vague, as it is in the maximal sense when we know noting other than the event in logically possible, no quantification is possible. To get numbers, we need specific information.
Enter the the Frequentist Fallacy. Happens like this. American citizens killed by shark bites are divided by the population, and this number is substituted for the probability of you yourself dying from shark bite. This “probability” is assigned to beach dwellers and Norther Michiganders alike. Which is silly, because, obviously, the information for these folks is radically different, and thus so are their (conditional) probabilities.
So is dying of a bee or wasp sting more probable than by shark bite? We now see that it makes no sense to ask this. If you can’t swim and are allergic to bee stings and live next to an apiary, then it’s more likely you’ll die from a sting than a shark bite. But if you live in Key West and go snorkeling daily and aren’t allergic to bees, it’s more likely you’ll die inside the innards of a shark.
How much more likely (in either case) we can’t say.
Thanks to Brad Tittle for suggesting this topic.