OK. Let’s make it even more extreme. Suppose you take a commercial flight. The likelihood of dying in a crash is on the order of 1 in 10 million. From a percent error or absolute error perspective, 99.99999% isn’t that different from 99% but that is the difference between one plane crash per year globally and a couple of dozen plane crashes per hour on average. These are wildly different in terms of acceptable safety.
OK. Let’s make it even more extreme. Suppose you take a commercial flight. The likelihood of dying in a crash is on the order of 1 in 10 million. From a percent error or absolute error perspective, 99.99999% isn’t that different from 99% but that is the difference between one plane crash per year globally and a couple of dozen plane crashes per hour on average. These are wildly different in terms of acceptable safety.
There’s a backup link in the comments: https://www.thejach.com/public/log-probability.pdf