What is the probability of success given two trials with a 1/16 chance each? I have never been able to wrap my head around probability, and I often find that my intuition is wrong.  In this case, I don't even have intuition as to where to begin.
If I have two trials, each with a 1/16 chance of success, what are the chances that either or both of them result in success?  How, mathematically, do you arrive at the correct probability?  How, intuitively, can I understand this number?

The probability that neither trial is successful is $(15/16)^2$ (assuming that the trials are independent), and the chances that at least one trial is successful is one minus that: $1-(15/16)^2 = 31/256$.
