Uber useful!!!
Estimating the chances of something that hasn’t happened yet
by John on March 30, 2010
Suppose you’re proofreading a book. If you’ve read 20 pages and found 7 typos, you might reasonably estimate that the chances of a page having a typo are 7/20. But what if you’ve read 20 pages and found no typos. Are you willing to conclude that the chances of a page having a typo are 0/20, i.e. the book has absolutely no typos?
To take another example, suppose you are testing children for perfect pitch. You’ve tested 100 children so far and haven’t found any with perfect pitch. Do you conclude that children don’t have perfect pitch? You know that some do because you’ve heard of instances before. But your data suggest perfect pitch in children is at least rare. But how rare?
The rule of three gives a quick and dirty way to estimate these kinds of probabilities. It says that if you’ve tested N cases and haven’t found what you’re looking for, a reasonable estimate is that the probability is less than 3/N. So in our proofreading example, if you haven’t found any typos in 20 pages, you could estimate that the probability of a page having a typo is less than 15%. In the perfect pitch example, you could conclude that fewer than 3% of children have perfect pitch.
via Estimating the chances of something that hasn’t happened yet — The Endeavour.