For a long time I've wondered about the significance of coincidences. How unlikely must a coincidence be before it should be accepted as some act of God/fate/whatever? It seems that if something, even if it can be explained by normal science, can occur at a rate that is absolutely beyond the realm of possibility (based on statistics) then perhaps this could serve as evidence of something bending reality towards its will.
For example: I grew up in Austin, TX and went to a day care during one summer at a place named Kids Computing (back in 1984). Years later I got a job programming in Boulder, CO (in 2001). After a couple of years working there I found that my boss was actually a worker at Kids Computing that summer while he was attending college at UT and we had actually first met when I was 5 years old 1000 miles away. What the heck are the odds of that? Especially when you consider he only worked there one summer, I only went there one summer, there was only about 5-7 staff members and there were only about 30 kids.
Another example would be the woman who hit a hole in one 14 times in 4 months. The odds against that are astronomical--it would be like winning the lotto 3 times in a row (or perhaps even less likely than that, it's difficult to calculate). All of the hole-in-ones had multiple witnesses with many of them occurring in competitions and the 14th in front of a television crew and caught it on tape. This seems like something MythBusters could test by building a ball-launching apparatus to shoot a golf ball with super-human control at the hole over and over again to see how often it could get a hole in one (making subtle changes in aim to get the perfect aim at the hole). If she was able to get a hole-in-one much more often than even this machine then surely it would have some significance, wouldn't it? (assuming MythBusters didn't screw up the experiment somehow)
While it's technically possible for something to occur, isn't there some point at which it's more likely that something is influencing the course of events than to believe otherwise? It's possible that when I flip a coin it will come up heads for the rest of my life. But if that happened, wouldn't that essentially prove that there is something beyond which we can currently explain occurring?