Table 2.1: Categorization of the adults in a small town Employed 460 Unemployed Total 40 Male 500 Female 140 260 400 Total 600 300 900 One of these individuals is to be selected at random for a tour throughout the country . (1) what is the probability of a man is chosen given that the person selected is employed? (2) what is the probability that the person chosen is an unemployed female?

This problem involves empirical probability. The table shows the breakdown of 98 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force. Marine Air Force Corps 8 12 5 17 Male Female Total Army 25 10 35 Navy 28 8 36 2 10 Total 73 25 98 The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is (Type an integer or decimal rounded to the nearest hundredth as needed.)

A sample of 200 new cars were checked for defects. The following table shows the results of the study.   Fewer than Six Defects Six or More Defects Total American Built 57 65 122 Foreign Built 36 42 78 Total 93 107 200 One car is selected at random. Round your answers to two decimals. (a) What is the probability a randomly selected car was American built?   (b) What is the probability that a randomly selected car had fewer than six defects, given that it is foreign built?   (c) What is the probability that a randomly selected car was American AND had six or more defects?   (d) What is the probability that a randomly selected car was American OR had six or more defects?

12. A survey conducted discovered that 63% of all Americans are overweight. Suppose that a number of randomly selected Americans are weighed. The following table may (or may not) be useful: k 0 1 2 3 4 1 4 6 4 1 4Ck (a) Find the probability that the 4th person weighed is the first person to be overweight. (b) Find the probability that it takes less than 4 people to observe the first overweight person. (c) Find the expected value and variance of the number of Americans that would have to be weighed in order to find the first person that was overweight.

Five thousand people were classified by their generation and their top pick for food cuisine. The results are provided below.   American Chinese Italian Mexican Millennials & Gen Z 300 380 220 1600 Gen X 200 250 100 450 Baby Boomer & Older 450 150 525 375   As needed, state answers to four significant figures.  If a person is randomly selected, what is the probability that the person is A member of Gen X?      A Millennial/Gen Z or had a top pick of Mexican Food?      A Baby Boomer/Older and had a top pick of Italian Food?     A Gen X given that the person picked American Food?     Picked Chinese Food given that the person is a Millennial/Gen Z?