Have you ever gone to the phone to call a friend, only to have the phone ring first and find your friend on the other end of the line? What are the odds of that? Not high, and your patternicity intuition probably signaled to you that there was something special about this event. Was there? Probably not. Here is why: the sum of all probabilities equals one. Given enough opportunities, outlier anomalies will inevitably happen. The question is not: What is the probability that a friend would phone while being thought about? - which is very low - but: In the total population of all people making phone calls and thinking about friends, what is the probability that at least one phone call will overlap with at least one simultaneous thought? - which is very high. Analogously, the chance of any one person winning the lottery is extremely low, but in the lottery system as a whole, someone will win. Coincidences are seen as miracles, and the pattern creates the illusion of purpose or reason.
Lets define a miracle as an event with million to one odds of occurring. Let us also assign a number of one-bit per second of data that flows into our senses as we go about our day, and assume that we are awake for 12 hours a day.
That nets us 43,200 bits of data per day, or 1,296,000 per month. Even assuming that 99.999% of these bits are totally meaningless (so we filter them out), that still leaves 1.3 "miracles" per month, or 15.5 "miracles" per year per person. Thanks for selective memory and the confirmation bias, we will remember only those few astonishing coincidences and forget the vast sea of meaningless data.
<3 Michael Shermer - The Believing Brain, pg 257