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My personal risk assessment strategy is to do something like: if my chance of car accident is 1/450 per year, would I pay one car accident in order to get 450 years of driving? If yes, then I drive. I do this for nearly all my risk assessments and I'm wondering how common it is.
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That's not how it works. If the chance of accident is 1/450 per year, your chance of going n years without an accident is (449/450)^n For 100 years it's about 80%.
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I'm not that schooled on probability, but I'm imagining a bunch of red dots, thousands of them. Randomly speckled in at an average of 1 every 450, there is a blue dot. What is the chance that, for any given red dot, there's at least 449 red dots between the blues on either side?
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With a sequence it's easier. Do coin tosses: the chance of one head is 0.5. The chance of two consecutive heads is (head AND head) = (0.5 * 0 5) = 0.5^2 = 0.25. For three consecutive heads it's 0.5^3 = 0.125, etc. Same thing with chances of having n years without an accident.
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