Mathematics
The Geometric Distribution: Waiting for the First Success
Quick fact
Even if the probability of success is high (e.g., 0.8), the expected number of trials until the first success is only 1/p, but the probability of needing more than the expected value is surprisingly large (about 37%).
Why this is interesting
Have you ever wondered how many tries you'll need before you finally roll a six? The geometric distribution gives a precise answer, and it often defies intuition.