Mark Greenaway writes:

If there's a probability p that something will happen when doing something once, then the probability of it having happened after having done it n times is 1 - p

^{n}. So there's an exponentially decreasing chance that you'll evade the risk you've been taking, every time you take it.

While the maths may be sound, the conclusion is not.

When you toss a coin it is unlikely that the next two tosses will both result in heads: a 1 in 4 chance. It is less likely that that you will toss four heads in a row: 1 in 16 chance. This is where it gets complicated, though. If you've already tossed two heads, that sequence of four heads is back down to 1 in 4. You've already traversed several of the unlikely possibilities and made them certainties. You now only have to traverse two more tosses and three unfavourable possibilities.

Every time you toss an unweighted coin there is a 50% chance of a head, and a 50% chance of a tail. The coin doesn't have a memory. It doesn't say "well, we're about due for a tail now". Even after a million tails, you still have a 1 in 2 chance of getting another tail. The sequence overall is unlikely, but the final toss is not.

The upshot is that while you can predict someone's risky behaviour will end in pain should they continue and even calculate the odds, the act of surviving the activity does not mean their end is closer or more likely than it was before. Statistics isn't relevant when it comes to this sample size of one. This is balanced by the fact that when someone dies due to risky activity the chance of death becomes a certainty, just as a survivor's chance drops to zero. Everyone who lives gets a fresh slate.

Benjamin