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

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

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

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

e. Given that 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?

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Population of city Region NE SE SW NW Under 50,000 50,000-500,000 Over 500,000 150 5350 35 15 5 60 90 70 30 25 30 60