Generally, you should not be in the habit of doing things that have a 0.1% chance of killing you. Do so on a daily basis, and on average you will be dead in less than three years
Indeed!
It’s even worse than that might suggest: 0.999^(3*365.25) = 0.334, so after three years you are almost exactly twice as likely to be dead than alive.
To get 50%, you only need 693 days, or about 1.9 years. Conversely, you need a surprising length of time (6500 days, about 17.8 years) to reduce your survival chances to 0.001.
The field of high-availability computing seems conceptually related. This is often considered in terms of the number of nines—so ‘five nines’ is 99.999% availability, or <5.3 min downtime a year. It often surprises people that a system can be unavailable for the duration of an entire working day and still hit 99.9% availability over the year. The ‘nines’ sort-of works conceptually in some situations (e.g. a site that makes money from selling things can’t make money for as long as it’s unavailable). But it’s not so helpful in situations where the cost of an interruption per se is huge, and the length of downtime—if it’s over a certain threshold—matters much less than whether it occurs at all. There are all sorts of other problems, on top of the fundamental one that it’s very hard to get robust estimates for the chances of failure when you expect it to occur very infrequently. See Feynman’s appendix to the report on the Challenger Space Shuttle disaster for amusing/horrifying stuff in this vein.
Very big and very small probabilities are very very hard.
Indeed!
It’s even worse than that might suggest: 0.999^(3*365.25) = 0.334, so after three years you are almost exactly twice as likely to be dead than alive.
To get 50%, you only need 693 days, or about 1.9 years. Conversely, you need a surprising length of time (6500 days, about 17.8 years) to reduce your survival chances to 0.001.
The field of high-availability computing seems conceptually related. This is often considered in terms of the number of nines—so ‘five nines’ is 99.999% availability, or <5.3 min downtime a year. It often surprises people that a system can be unavailable for the duration of an entire working day and still hit 99.9% availability over the year. The ‘nines’ sort-of works conceptually in some situations (e.g. a site that makes money from selling things can’t make money for as long as it’s unavailable). But it’s not so helpful in situations where the cost of an interruption per se is huge, and the length of downtime—if it’s over a certain threshold—matters much less than whether it occurs at all. There are all sorts of other problems, on top of the fundamental one that it’s very hard to get robust estimates for the chances of failure when you expect it to occur very infrequently. See Feynman’s appendix to the report on the Challenger Space Shuttle disaster for amusing/horrifying stuff in this vein.
Very big and very small probabilities are very very hard.