Exactly. Probabilities are calculated by ignoring potential commonalities, yet when accidents happen, they are rarely due to the occurrence of a single event. A chain of even extremely low probability events, that certainly must share some kind of of commonality, can occur that seemingly integerate into a resulting catastrophy of a far higher probability than you would get, if all such events in the chain were considered to have been independent. Probabilities of events resulting from chaining independent events lead us to believe that they are even less likely to occur, if not practically impossible, than if a chain did not cause the event. Continuing with customary examples, the probability of drawing a royal flush, a chain of independent events, is practically impossible during the finite time limit of my poker game night, unless I bring some extra cards to the table, which you all might suspect, if I turned up with one in your game parlor. That is the same logic that brought on the 737 Max investigation. Two crashes occurring within a short timespan looked suspicious. Why? Because that result was impossible when assuming independent event calculations. Yet, even though it was theoretically (nearly) impossible, that result actually occurred and triggered the "class action" investigation. My question now is, why did not the occurrence of just one event initiate such an investigation? Should not the occurrence of one very unlikely event automatically suggest that the calculations were amiss and further action might immediately be needed. In fact the more unlikely the event, the more immediate the need may be. That leads me to believe that even calculating a probability of an extremely unlikely event could be cause for concern and might in itself warrent a deeper study into how valid such a calculation really might be, especially if it involved chaining a number of supposedly "independent" events. The underlying problem is that probabilities are calculated using actual (or simulated actual) events and that extreme events, by definition, dont happen enough to obtain good models of them. So is there some kind of factor we miss when chaining independent events? Should probabilities of chained independent events be modified by 1/ψ * number_of_events, or n^2, or some other factor to account for dependent complexities in models that are not fully well understood?
