A fast-food restaurant chain has 600 outlets in the United States. The following table categorizes cities by size and location, and presents the number of restaurants in cities of each category. A restaurant is to be chosen at random from the 600 to test market a new style of chicken.

a. If the restaurant is located in a city with a population over 500,000, what is the probability that it is in the Northeast?

b. If the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000?

c. If the restaurant is located in the Southwest, what is the probability that it is in a city with a population of 500,000 or less?

d. If the restaurant is located in a city with a population of 500,000 or less, what is the probability that is in the Southwest?

e. If the restaurant is located in the South (either SE or SW), what is the probability that it is in a city with a population of 50,000 or more?