Yes, Laplace’s rule works in this instance. Assume you have a printer that prints out papers that say either “yes” or “no”, each independently identically distributed with unknown (and uniformly distributed) p. If you pull the papers directly from the printer you have a classic Laplace’s rule situation. If you print out N papers without looking at them, then look at each in turn, the situation is essentially unchanged. Furthermore, the probability that k of the N papers say “yes” is the same for each 0 ⇐ k ⇐ N.
Yes, Laplace’s rule works in this instance. Assume you have a printer that prints out papers that say either “yes” or “no”, each independently identically distributed with unknown (and uniformly distributed) p. If you pull the papers directly from the printer you have a classic Laplace’s rule situation. If you print out N papers without looking at them, then look at each in turn, the situation is essentially unchanged. Furthermore, the probability that k of the N papers say “yes” is the same for each 0 ⇐ k ⇐ N.