U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census

Bureau)

a. Randomly selecting someone who is under 10 years old

19. U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census

Bureau)

c. Randomly selecting someone who is not 60 years or over

Marijuana Use The percent distribution of the last marijuana use (either medical or nonmedical) for a sample of 13,373 college students is shown in the pie chart. Find the

probability of each event. (Source: American College Health Association)

a. Randomly selecting a student who never used marijuana

Marijuana Use The percent distribution of the last marijuana use (either medical or nonmedical) for a sample of 13,373 college students is shown in the pie chart. Find the

probability of each event. (Source: American College Health Association)

d. Randomly selecting a student who has not used marijuana within the last 12 months

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)

b. Randomly selecting a person from the sample who is conservative or very conservative

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)

d. Randomly selecting a person from the sample who is either unsure or moderate

22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the

probability of each event. (Adapted from Ipsos)

b. Randomly selecting a British adult who feels that the move has had a very negative impact on Great Britain

22. Brexit A survey asked 1115 British adults how Britain's decision to leave the European Union has impacted the country. The results are shown in the Pareto chart. Find the

probability of each event. (Adapted from Ipsos)

d. Randomly selecting a British adult who feels that the move has had a fairly positive or very positive impact on Great Britain

23. Engineering Degrees The table shows the numbers of male and female students in the U.S. who received B.S. degrees in engineering in a recent year. A student earning a B.S. degree in engineering during that year is selected at random. Find the probability of each event.

(Source: National Center for Educational Statistics)

c. The student is not female or did not receive a mechanical engineering degree.

"True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false,

explain why.

3. When two events are mutually exclusive, they have no outcomes in common."

True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

3. A combination is an ordered arrangement of objects.

56. Defective Disks A pack of 100 recordable DVDs contains 5 defective disks. You select four disks. What is the probability of selecting at least three non defective disks?

1. When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting? Give an example.

True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

6. 7C5=7C2

In Exercises 7-14, perform the indicated calculation.

9.8C3

In Exercises 7-14, perform the indicated calculation.

12. (10C7)/(14C7)

In Exercises 15-18, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.

15. The number of ways 16 floats can line up in a row for a parade

In Exercises 15-18, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.

17. The number of ways 2 captains can be chosen from 28 players on a lacrosse team

20. Skating Eight people compete in a short track speed skating race. Assuming that there are no ties, in how many different orders can the skaters finish?

23. Footrace There are 72 runners in a 10-kilometer race. How many ways can the runners finish first, second, and third?

25. Playlist A band is preparing a setlist of 21 songs for a concert. How many different ways can the band play the first six songs?

28. Necklaces You are putting nine blue glass beads, three red glass beads, and seven green glass beads on a necklace. In how many distinguishable ways can the colored beads be put on the necklace?

31. Experiment A researcher is randomly selecting a treatment group of 10 human subjects from a group of 20 people taking part in an experiment. In how many different ways can the treatment group be selected?

34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.)

37. Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Use technology to find how many ways one polluted lake and five nonpolluted lakes can be chosen.

Board of Directors The University of Colorado Board of Directors has 23 members. One member serves as board chair and another serves as vice chair. Given the names of the 23

board members, what is the probability of randomly selecting the name of the chair and the name of the vice chair? (Source: University of Colorado)

Shuffle Play You use a shuffle playback feature to randomly play songs in a playlist. The playlist of 56 songs includes 15 instrumental songs.

a. What is the probability that the first three songs to play are instrumental songs? (Assume a song cannot be repeated.)

Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team.

b. What is the probability that none of the offices are filled by members of the debate team?

50. Investment Committee A company has 200 employees, consisting of 144 women and 56 men. The company wants to select five employees to serve as an investment committee.

a. Use technology to find the number of ways that 5 employees can be selected from 200.

50. Investment Committee A company has 200 employees, consisting of 144 women and 56 men. The company wants to select five employees to serve as an investment committee.

d. Explain how the company can select a representative sample of the male and female population of employees.