The two examples, coin and Lincoln rock, use two different concepts of probability.
- The coin example knows the probability 1/2 for the head of a fair coin. Accordingly it computes the probability of two heads in sequence as 1/4 = (1/2) x (1/2).
- The Lincoln example does not know the probability that an arbitrary rock is a Lincoln rock. Not only that one does not know the probability. The probability is not well-defined. One speaks only informally about the probability of a LinolnLincoln rock.