Final answer:
a. The experiment ends with probability 1 because there are a finite number of possible outcomes. b. Construct a Markov chain to calculate the probability of seeing HH before HTT. c. Find the expected time until hitting either HH or HTT.
Step-by-step explanation:
a. The experiment ends in a finite time with probability 1 because there are a finite number of possible outcomes. In this case, the experiment ends when Maria sees either the sequence HH or HTT. Since the coin flips are independent events and the coin is fair, each flip has a 1/2 probability of landing on heads or tails. Therefore, the probability of seeing either HH or HTT eventually is 1 - (1/2)^2 - (1/2)^3 = 7/8, which is greater than 0.
b. To construct a Markov chain, we can consider the following five states: 1. HH was obtained before HTT; 2. HTT was obtained before HH; 3. neither HH nor HTT occurred already, and the last letter is H; 4. neither HH nor HTT occurred already, and the last two letters are HT; 5. neither HH nor HTT occurred already, and the last two letters are TT. The transition probabilities between these states can be determined based on the probabilities of flipping heads or tails. By calculating the probabilities for each state, we can determine the probability that Maria sees HH before HTT.
c. To find the expected time until hitting either HH or HTT, we can calculate the expected time for each of the five states in the Markov chain. By multiplying the probabilities of each state by their respective expected times and summing them, we can find the overall expected time. We should exclude the first three flips that showed TTT.