1. Let's eat: A fast-food restaurant chain has 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 to test

market a new menu. Round your answers to four decimal places.

Population

Part 1 of 5

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

Part 2 of 5

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

Part 3 of 5

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

Part 4 of 5

Given that the restaurant is located in a city with a population of or less, the probability that it is in the Southwest is. 500,00

Part 5 of 5

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

2. In a recent school year in the state of Washington, there were 325,00 high school students. Of these, 158,000 were girls and 167,000 were boys. Among the girls, 67,000 dropped out of school, and among 10,200 the boys, dropped out. A student is chosen at random. Round the answers to four decimal places.

(a) What is the probability that the student is male?

(b) What is the probability that the student dropped out?

(c) What is the probability that the student is male and dropped out?

(d) Given that the student is male, what is the probability that he dropped out?

(e) Given that the student dropped out, what is the probability that the student is male?

3. Quality control: A population of semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population. Write your answer as a fraction or a decimal, rounded to four decimal places.

(a) What is the probability that the wafer is from Lot A?

(b) What is the probability that the wafer is conforming?

(c) What is the probability that the wafer is from Lot A and is conforming?

(d) Given that the wafer is from Lot A, what is the probability that it is conforming?

(e) Given that the wafer is conforming, what is the probability that it is from Lot A?

(f) Let be the event that the wafer comes from Lot A, and let be the event that the wafer is conforming. Are and independent?

4. An unfair coin has probability 0.3 of landing heads. The coin is tossed five times. What is the probability that it lands heads at least once? Round the answer to four decimal places.

P(Lands heads at least once) =