Let's eat: A fast-food restaurant chain has 597
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
597
to test market a new menu. Round your answers to four decimal places.
Population
of City Region
NE SE SW NW
Under
50,000 26 37 15 4
−50,000500,000 55 95 66 32
Over
500,000 152 23 35 57

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(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?