You're apparently the one who doesn't understand how statistics/probability works. You're correct about his chance of dying once, but there's also a chance of dying twice, a chance of dying 3 times, etc. The expected value of the number of times he would die is 5000(1/1000), or 5.

If you replaced "deaths" in your post with "coin flips", this becomes obvious. I'll repeat your post with some different numbers so you can see how absurd your argument is.

    If you have a 1/2 chance of flipping heads and you flip 10 coins, you won't get 5 heads.

    You will have 1-(1/2)^10 of flipping heads, that [sic] 99.902%. That's not 1. So you won't get 5 heads.

See how that doesn't make sense?

Now, obviously a real person can't die more than once, but if you think he was mistaken about that then his supposed error has more to do with biology than statistics. Any reasonable reader would understand that it was just his rhetorical way of describing a large number of independent statistical events. If it helps, think of it as a population of 5000 equally-careless people taking 1 shower each, not a single person taking 5000.

Sorry, I understand what you're trying to say, but I don't think your example serves your point.

I don't think I mixed up expected value and probability of occurrence, if I did please point out where.

You don't care too much about expected value because once the event occurs (death), you can't play anymore...

If you were playing money, on the other hand, expected value would be much more interesting.

I think probability is interesting because if you say "I'll take the shower 2,500 times instead of 5,000" you drop the probability of death to 91.8 % (from 99.9%)...

If you say I'll die on average only 2.5 times you say nothing interesting.

He actually says "I’d die or become crippled about five times before reaching my life expectancy." Being crippled does not necessarily preclude you from taking a shower. Therefore, if you look at his expected value of "having a significant fall in the shower" instead of "dying in the shower", it doesn't have the same problem of being impossible. Obviously all 5 can't be fatal events.

That's a relief, I prefer only dying once. Pedantic silliness aside, it was clearly an illustration of how frequency can amplify small probabilities to near-certainties, evidenced by the repetitive use of the one-in-a-thousand statistic.

Just another name for Murphy's Law :)

I'm willing to bet that Jared Diamond understands statistics. He just understands that most of the people reading his article don't. The inaccuracy doesn't affect the article so it's better to be more clear than completely inaccurate.

The thing is, it's not even an inaccuracy. He's entirely correct (statistically speaking). He's describing the concept of Expected Value* without explicitly using the term.

The only thing he could be said to "wrong" about is the idea that a person can die more than once, but everybody understands that that's not actually true. It certainly doesn't "ruin the article" like this poor fellow seems to think.

* http://en.wikipedia.org/wiki/Expected_value

The other key thing is that the risk he mentioned was not specifically of dying, but of either death or being crippled. Both of those are very frightening prospects, and he simplifies it as "dying five times" when he does the calculation.

Expected value gives you the "If I look at 5000 shower-takings with a 1/1000 probability of a shower-taking resulting in death, I expect to see 5 deaths on average". Of course when applying it to a single lifetime, the correct thing to consider is "If I take showers until I have taken 5000 showers or died, what is the expected number of shower-deaths I will incur", which is .9972.

I guess to die 99,32% is not dying at all, so you actually die never. Taking a shower is perfectly save.

And surprisingly enough, if you add the many-worlds quantum theory[1] that is exactly what you get. Non-death.

1)http://en.wikipedia.org/wiki/Multiverse#Level_III:_Many-worl...

> Life expectancy for a healthy American man of my age is about 90. (That’s not to be confused with American male life expectancy at birth, only about 78.)

It's interesting that Diamond literally describes the survival function[0], which is usually thought of as E[X|x>=a], but then conflates this with the expected value in the next breath.

I'm confident he understands the difference, but the notion of the survival function is so easy to understand without the underlying statistics (as he explains in two sentences), and provides a much more useful way of conceptualizing statistics. (Expected values of binomial distributions, on the other hand, are highly useful mathematically but difficult to conceptualize without the underlying statistics).

[0]http://en.wikipedia.org/wiki/Survival_function