Approaching the Reciprocal of the Natural Log Base ("e")
Say the chance of a certain occurrence is 1 / n. What are the odds that the occurrence will NOT take place at least once during n trials?For instance: you're hitchhiking, and the odds that any particular car will pick you up are 1 / 100. What are the odds that the next 100 cars will pass by without anyone giving you a ride?
As n increases, the likelihood that you won't get a ride approaches 1 / e (about 36.79%). Click here for one of a number of mathematical explanations available online.
In the context described above, your risk of not getting a ride from n cars will be only a little less than 1 / e, unless n is very small. With just 24 cars, the risk exceeds 36%, but it can never reach 37%! Try it out, below, for 1, 2 , 3, ... 1000, ... 9,999,999* cars: