The It department at a large company allows employees to choose either a HP laptop, a dell laptop, or an apple MacBook. At the end of each financial year, the IT department recalls and replaces all computers. With probability 0.6, employees will request the same brand of computer again. An employee will switch to an Apple MacBook with probability 0.3 if they just had a HP laptop; and with probability 0.4 if they just had a Dell laptop. If they had an apple MacBook they are equally likely to switch to either a HP or Dell laptop.

1. Model the problem as a Markov chain with three states (HP, Dell, Apple) and give the transition probability matrix.
2. If a randomly chosen employee is currently using a HP laptop, what is the probability that they will also be using a HP laptop in 2 years' time?
3. What is the long-term distribution of laptop brands used by employees in the company ?