In a small town there are two places to eat: 1) a Chineserestaurant and 2) a pizza place. Everyone in town eats dinner atone of the these two places or eats dinner at home.

Assume the 20% of those who eat in the Chinese restaurant go tothe pizza place the next time and 40% eat at home. From those whoeat at the pizza place, 50% go to the Chinese restaurant and 30%eat at home the next time.  From those who eat at home,20% go to the Chinese restaurant and 40% to the pizza place nexttime. We call this situation a system. This system can be modeledas a discrete-time Markov chainwith threestates.

1. Define the three states and write down the one-step transitionprobability matrix.
2. If a family has decided to eat dinner in the Chinese restaurantwith the probability of 0.05 or in the pizza place with theprobability of 0.15 today, what is the probability that this familywill eat dinner at home in two days
3. If a lady is having pizza today, how long will it take for herto have pizza again
4. Given that a man has been eating at the Chinese restauranttoday and yesterday, on average, how long will it take for him toeat at the pizza place for the first time?
5. If a family plans to eat at home on Sunday, what is theprobability that they will eat Chinese on Tuesday (same week) forthe first timethen they will eat Pizza on Friday(same week) for the first time?