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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.

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