Mathematics — Probability · absorbing-markov-chains
Problem
We can use the gambling interpretation given in Exercise 28 to find the expected number of tosses required to reach pattern B when we start with pattern A. To be a meaningful problem, we assume that pattern A does not have pattern B as a subpattern. Let EA(TB) be the expected time to reach pattern B starting with pattern A. Using the formula EA(TB)=BB−AB, verify that this gambling interpretation leads to the correct answer for all starting states in the examples that you worked in Exercise 28.