Taxis pick up and deliver passengers in a city that is divided into three zones. Records kept by the drivers show that, of the passengers picked up in zone I, 50% are taken to a destination in zone I, 40% to zone II, and 10% to zone III. Of the passengers picked up in zone II, 40% go to zone I, 30% to zone II, and 30% to zone III. Of the passengers picked up in zone III, 20% go to zone I, 60% to zone II, and 20% to zone III. Suppose that, at the beginning of the day, 60% of the taxis are in zone I, 10% in zone II, and 30% in zone III. What is the distribution of taxis in the various zones after all have had:.
1. one passenger?
2. Two passengers?
3. Twenty passengers?