In the 1970’s, a controversy arose about a probability problem posed by Irving Copi. One side argued that a common spontaneous intuition about the problem is correct; the other side argued that this intuition is mistaken. Here, I argue (1) that the naïve intuition yields the correct answer, but accidentally and for a wrong reason; (2) that a more reflective intuition yields a wrong answer, and hence, is also mistaken; and (3) that an even more reflective intuition yields the correct (...) answer for a correct reason. This warrants what I call optimistic fallibilism concerning intuitions about probability: although intuition is certainly prone to error in this domain, intuition has the capacity for self-correction. A naïve intuition that is mistaken can be replaced by a distinct, reflective intuition; and a reflective intuition that is mistaken can be replaced by another reflective intuition – with the process ultimately yielding a sound intuition. (shrink)

In an article “Countering a Counter-intuitive Probability” [4], Lynn E. Rose discusses a question in conditional probability, claiming that the following problem posed by Copi [1] is usually incorrectly solved:Remove all cards except aces and kings from a deck, so that only eight cards remain, of which four are aces and four are kings. From this abbreviated deck, deal two cards to a friend. If he looks at his cards and announces that his hand contains an ace, what is the (...) probability that both his cards are aces? If he announces instead that one of his cards is the ace of spades, what is the probability then that both his cards are aces? (shrink)