If there were no such things as coincedences then we wouldn't have a word for it.

If DaveO's son had broken his hip on another day - in what is a fairly average sounding injury - would he have thought it any more or less unlucky?

My son ran into a tennis net corner post and broke his collarbone. Hundred thousand to one chance, but it happened. Not a Friday 13th, but well.....

In an infinite world, anything is possible. In a world containing billions of people doing billions of different things, most things are possible over enough time.

Or, if you prefer, typewriters and monkeys.

Some people may be trying to take all this too seriously, but although I don't know what it is, or imagine what it might even be, my years on the planet have convinced me there is something in some of this stuff - such as 13. I'll give you another example. Say you are speaking to someone about an event. If those participating can't hear you, then surely what you say can't possibly influence an outcome in any way whatsoever? I'd agree with that. BUT . . . I am also at the same time entirely convinced that there is something weird in the phenomenon usually rreferred to as "Commentator's Curse", or "hexing". Like the number 13 thing, it happens just that bit more regularly than it should to be pure coincidence.

If you want a belly laugh, type in "John Virgo Demonstrates The Commentator's Curse On Mark Allen (2011 Masters)" in a popular video site

People's estimates of probability are usually hopelessly inaccurate and often laughable. Hence the existence of casinos, bookies, the lottery etc.

Part of the problem is the subjectivity involved when considering 'amazing' events/ coincidences. You will tend to remember and highlight anything bad that happens on Friday the 13th for example. If the same thing happened any other day you simply wouldn't make the link to the date. The same thing happens when people are amazed if they bump into someone they were 'just thinking about'. This becomes a seemingly miraculous event - ignoring entirely all the other times they were thinking about someone but didn't bump into them for example.

I believe it is poppycock.
In my ever so humble opinion, there is no such thing as fate.
And even if there was and fate being something like 'that which is inevitably predetermined', how can you tempt (presumably meant to mean invoke) it .
Surely your fate is your fate, it's predetermined and you can't alter it by invoking it.
If you can alter it, then there is no such thing as fate. If you want to walk in front of a train and alter the course of your existence, you can decide to do so at any time.
But of course some people would argue that you were meant to do that all along ... wouldn't they?

Working with traffic and traffic management i find Friday the 13th a day with high accident numbers and plenty of traffic problems BUT i also find Fridays of any date very busy and full of accidents.
Plus an extra factor of Friday the 13th is the self fulfilling prophecy, they think therefore they do.