Flip a fair coin again and again. Can you be absolutely sure that the fraction of heads will eventually settle near one‑half, and stay there? What if we run a sequence of experiments — will a particular rare pattern pop up infinitely often, or just a few times before vanishing forever? The answers lie in two key ideas of probability: the Borel–Cantelli lemmas and the laws of large numbers. Together they reveal the important long‑run behavior of random phenomena.