Suppose that I open the newspaper and read that a truck full of tomatoes crashed and spilled all over the freeway. At that moment my wife approaches me with a bowl full of tomatoes , trips and they all land in my lap. Ten minutes later, after I am all washed up, my wife tells me that her friend Mary just bought a store. Immediately the phone rings and it is a wrong number asking for Mary ( not the Mary my wife referred to) . Now, obviously these are just weird coincidences. However, suppose that every ten minutes another coincidence occurs and every ten minutes after that. The coincidences are unrelated to each other. It would seem safe to assume that if such coincidences happen every ten minutes for 20 years something is going on. My question is, is there a mathematical way to determine at what point the amount of coincidences become worthy of investigation? Note that I am not asking for the probability of a particular coincidence, I am asking for the probability that a certain amount of coincidences will happen. Just as meta-language is language about language, this could possibly be described as meta-probability.
Re: Meta-probability The standard usually used in statistics is the 95% confidence level. If you experience events that would, by chance, only happen 5% of the time it's 'worthy of investigation'. But you need to be careful in what you consider before doing the calculation! For example, consider the expected number of such occurrences over the last five years, not over just that day; consider not just the particular event that happened but others that you would have also considered coincidental. The chance of rolling 6, 5, 4, 3, 2, 1 in six consecutive dice rolls is only 1/50,000 or so, but what other combinations would you have considered strange -- and how many dice do you roll? How many names do you hear out of the blue, and how long after an occurrence like that would you consider it strange? Etc.