Suppose that demographic studies show that each year about 8 of a city's population moves to the suburbs (and 92 stays in the city), while 4 of the suburban population moves to the city (and 96 remains in the suburbs). In the year 2000, 64.
1 of the population of the region lived in the city and 35.9 lived in the suburbs. What percentage of the population of the region would eventually live in the city if the migration probabilities were to remain constant over many years? For simplicity, ignore other influences on the population such as births, deaths, and migration into and out of the region.
A) 41.7 B) 33.3 C) 50 D) 66.7
Question 2
Suppose that the weather in a certain city is either sunny, cloudy, or rainy on a given day, and consider the following:
1. If it is sunny today there is a 70 chance it will be sunny tomorrow and a 30 chance that it will be cloudy.
2.
If it is cloudy today there is a 40 chance it will be sunny tomorrow, a 40 chance that it will be cloudy, and a 20 chance that it will be rainy.
3. If it is rainy today there is a 40 chance it will be sunny tomorrow, a 30 chance that it will be cloudy, and a 30 chance that it will be rainy.
Suppose the predicted weather for Friday is 50 sunny, 30 cloudy, and 20 rainy. What are the chances that Sunday will be rainy?
A) 10.2 B) 12 C) 9.2 D) 13
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