 We face essentially this problem when we frame the problem of induction in probabilistic terms. Earlier we saw two competing ways of assigning prior probabilities to sequences of coin tosses. One way divides the possible outcomes according to the exact sequence in which \(\mathsf{H}\) and \(\mathsf{T}\) occur. The PoI assigns each possible sequence a probability of \(1/1024\), with the result that the first 9 tosses tell us nothing about the 10th toss. The second, Carnapian way instead divides the possible outcomes according to the number of \(\mathsf{T}\)s, regardless of where they occur in the sequence. The PoI then assigns each possible number of \(\mathsf{T}\)s the same probability, \(1/11\). The result then is that the first 9 tosses tell us a lot about the 10th toss: if the first 9 tosses are tails, the 10th toss has a \(10/11\) chance of coming up tails too.