Coincidence

[This will be a small rant from a Mathematician's perspective, a fair warning.]

The word 'coincidence' is defined as "a remarkable concurrence of events or circumstances without apparent causal connection" or as a "correspondence in nature or in time of occurrence."  

Too often I hear people use the word coincidence as something contrary to "God's will" or "the great plan." How can it be a coincidence when God exists? How can anything be so random? How can anything like that occur? 

Before I move on, let me define probability for you. It's a rather simplistic definition but necessary nonetheless. 1) Probability is the chance that something will happen - how likely it is that some event will happen. 2) The probability of an event is the measure of the chance that the event will occur as a result of an experiment. The probability of an event A is the number of ways event A can occur divided by the total number of possible outcomes. It is important to remember that probabilities do not tell you what will happen, only what is likely to happen. The distinction is very necessary. So when you say that the probability of Heads or Tails in a fair coin is .5 or 50%, you are essentially saying that if you keep flipping the coin and add all those probabilities, it adds up to or comes close to .5 or 50%. It is likely that there if a 50/50 chance of you getting Heads or Tails. It is unlikely, although not impossible, to flip a coin 20 times and get 20 Heads.

The chance of you getting hit by lightening is 1 in 700,000 in the U.S. What this means is that out of 700,000 times that lightening strikes in the U.S., the chance of you getting hit by it is once. That is the probability. You can call it coincidence or God's will or whatever you like, that's your prerogative. 

My problem is with the idea of devaluing the word 'coincidence.' Something is too much of a coincidence. Something occurring that simply can't happen without a greater will involved. The reason I have a problem with that is because it is taking the Math out of the equation and deeming it a farce. When you say the odds are too small for it to be a coincidence, you are denying the principles of Mathematics. You are saying that the Mathematical principles allow for this situation to exist are false simply because your mind is incapable of accepting the odds. The thing is, Mathematics isn't bound by the rules of this universe. You can adjust the variables and constants and go in dimensions our mind is incapable of imagining. Math allows you to consider alternate universes. So by saying, X is too big of a coincidence, you are insulting the principles of Mathematics. When Mathematicians calculate the probability of an event, that probability exists based on past events. It's deductive in nature. Dismissing that because your mind is incapable of understanding the odds is scientifically, and thus mathematically, inaccurate. The probability exists, not for your convenience, but because it is in nature. When you study Probability, you are told two things over and over again. 1) Correlation doesn't mean causation, and 2) You can never get a perfect probability of 1. The reason for the second statement is the possibility of not having recorded for any outliers. So Math accounts for any room there exists for an error. That's why you often see Mathematicians use terms like "almost surely" instead of "surely." It seems like a simple difference of one word but within that word lies an entire frame of reference. You are almost sure something happens but not sure because you are accounting for that freak chance where that thing deviates from the norm. And this is why saying something is too much of a coincidence is redundant and contrary. It can't be too big of a coincidence when it is a coincidence by nature. It can't be a coincidence and defy nature because nature already accounts for the possibility of that event happening.

P.S Correct me if you see any mathematical inaccuracies, I am but a student.