Truist Bank was opened across the street from the Bank of Texas (BoT) last year. They know that they have competition from the BoT in terms of market share. After doing some basic research on the habits of their customers, they found that if a customer banked at Truist in a given month, the probability of the customer returning to Truist in the following month is 0.75 and the probability that the customer banks at BoT in the following month is 0.25. However, if a customer banks at BoT in a given month, the probability of the customer returning to BoT in the following month is 0.87 and the customer going to Truist in the following month is 0.13. Suppose that they want to consider the Markov process associated with the monthly banking habits of one customer, but they do not know where the customer banked in the previous month. Thus, they assume a 50% probability that the customer banked at Truist or BoT (that is to say, ₁(0) = 0.5 and ₂(0) = 0.5). Given these initial state probabilities, answer the following questions:

1. The probability that the customer banks at Truist Bank in Month 2 = (Four decimal places)
2. The probability that the customer banks at BoT in Month 6 = (Four decimal places)
3. What is the long-run probability (or market share) of Truist Bank? % (write in percent terms with two decimal places)
4. Truist Bank considers running a promotion to attract BoT customers by offering a $10 gift card for banking with Truist, resulting in the probability of BoT customers going to Truist to increase from 0.13 to 0.20 in the next month. What would be the new market share of Truist Bank now? % (write in percent terms with two decimal places).