Shown in this image is an equivalency between two ways of calculating the probability of achieving within x tries some outcome with a constant probability of 1/x, where x must be a natural number.
For instance, for x = 2, this image shows an equivalency between two ways of calculating the probability that if you flip 2 coins, you'll get heads on at least one of them.
Or for x = 6, it shows an equivalency between two ways of calculating the probability that if you roll 6d6, you'll roll at least one 6.
I was interested in this mathematical question because probabilities are often expressed in terms of "out of," e.g. there is a "1 out of 2" chance of landing heads on a flipped coin, which would seem to imply that if you flip 2 coins, you're guaranteed to get exactly 1 heads, which is obviously not actually true. I was interested in what the actual likelihood is that any given experiment will yield the desired outcome in exactly the expected ratio.
