From time to time, I encounter individuals making an argument when they don’t really understand how statistics work. This happens most frequently in discussions about visits by E.T. aliens or the inappropriate uses of quantum mechanics. When a chain of events is required to occur before something can be witnessed, the resultant probability is the multiplication of all the individual probabilities. As a concrete example, let us say we buy a lottery ticket where the odds of winning the jackpot are 1 in a million. What are the chances of winning 2 jackpots if only 2 tickets are purchased? Answer: one in a million-million (i.e. one in a trillion). The odds of buying only 4 tickets and winning the jackpot 4 times: one in a trillion-trillion. At what point is it appropriate to say that’s impossible? If someone won 4 jackpots off 4 tickets purchased, there would be a corruption investigation, seeking to find out how the person was cheating. Someone is likely to go to prison even if no crime had been committed. I feel justified in saying: it’s possible, but it will never happen.
Similarly, there are a number of highly improbable conditions that must occur prior to any extraterrestrial civilization can be observed visiting Earth. Multiplying highly improbable by other highly improbables leads me to conclude that it has not happened, especially since there is no credible evidence Earth has been visited. While each condition is technically possible, it would be a big mistake to conclude that anything that is possible must have already happened. Such an outcome (actually being visited) is so improbable that I’m more likely to win either the MegaMillions or Power Ball jackpots ten times. I’m not going to hold my breath.