 We can exploit this freedom and get more sensible, induction-friendly results if we assign prior probabilities using a different scheme advocated by Carnap (1950). Suppose instead of assigning each possible sequence the same probability, we assign each possible number of \(\mathsf{T}\)s the same probability. We could get anywhere from 0 to 10 \(\mathsf{T}\)s, so each possible number of \(\mathsf{T}\)s has probability 1/11. Now, there’s just one way of getting 0 \(\mathsf{T}\)s: