I caught my son counting his ribs during a biology exam. As punishment for this act of cheating, I set him in the corner with a fair coin and told him he must stay in the corner, flipping the coin, until it comes up heads. The expected number of flips to the first success is, of course, 2.
Can I argue that his sentence will be completed in a finite number of coin flips?
Can it be argued that I potentially sentenced him to an eternity of flipping that coin because the probability of an infinitely long run of tails is infinitesimally larger than 0?