I think we can all agree that if you flip a coin, the chances of getting either heads or tails are 50%, no matter how many times you flip it. But let's say you flip it, and get a tails. If you flip it again, what are the odds of getting another tails?

If you said 50%, you would be wrong. How is that possible? It's because the odds of getting two tail flips in a row are only 25%, even though the odds of getting a tails result on either flip are 50%. If you just look at a given flip in isolation, the odds of getting one specific result are going to be 50%, and never change. But if you take a set of flips, the odds of continuing to get that specific result (or more accurately, of not getting a specific result) drop every time you flip. It's the same reason that you only have a 1/6 chance of rolling a 6 on a six-sided dice, but you have a 11/36 chance of rolling at least one 6 if you roll two six-sided dice.

The formula for figuring it out is surprisingly simple. It's x^{n}/y^{n}, where x is the number of results that aren't the one you're aiming for, y is the number of total results, and n is the number of tries you've made. For a coin flip, it's simple; x is always going to be 1, because 1 to any power remains 1. So it's simply dividing 1 by successive powers of 2. For a dice roll (like that six-sided dice I just mentioned), it gets a bit trickier, because x increases along with y, but since x is always smaller than y, the ratio of x^{n} to y^{n} decreases as n increases.

What's even more fun is that you can use this for other things, like, say, the probability of life existing on other planets, or the probability of life occurring on its own. Naturally, it's not realistic to figure out the exact odds, since there are several things that we can't properly quantify, but we can figure out approximate odds and then run them through the formula to get the odds of it happening over time. I don't have access to a powerful enough calculator to actually calculate meaningfully long odds (like some of the ridiculously huge odds creationists like to give about abiogenesis happening), but I think this shows that even when the chances are initially tiny, provided you have enough opportunities for it to happen, it will eventually become very likely to happen.