In their paper ‘Methods for Studying Coincidences, ‘ Diaconis and Mosteller propose the law of truly large numbers, which states that almost any outrageous event is bound to occur with a large enough number of independent samples!
Imagine an event that happens with a probability of 0.1% or 0.001. Therefore, the chance that it doesn’t happen is 0.999. If you carry out 100 independent trials, the probability of this not occurring is 0.999100 = 0.90. In other words, there is a 1-0.9 = 0.1 or 10% chance of occurrence. The following is the plot of this from 1 to 10,000 trials.
You can see that beyond, say, 5000 independent trials, this rare event is sure to occur at least once.
