Download Chapter 13 Review Worksheet

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Date __________
Statistics Chapter 13: Review A
1. Give a definition and example in your own words for each of these concepts.
a. Law of Large Numbers
b. The non-existent law of averages
c. Fundamental Counting Principle (for and & or)
d. Permutation
e. Combination
2. A game has two possible outcomes—win or lose. Explain when the chance of winning will not be 50%.
3. There are 5 different burgers and 8 different milkshakes on a menu.
a. How many ways can you order one burger and one milkshake?
b. How many ways can you order one burger or one milkshake?
4. Twenty different videos will be shipped via several boxes. Three videos will be randomly selected and
assigned to box A. How many different sets of videos are possible for box A? Show your work.
5. There are 12 people on a basketball team, and the coach needs to choose 5 to put into a game. Show work.
a. How many different possible ways can the coach choose a team of 5 players?
b. If the coach chooses the 5 players at random, what is the probability that the team captain is chosen?
You must show how to set up this problem but you can use the short-cut key to evaluate the answer.
6. In a game, each player receives 7 cards from a deck of 52 different cards. How many different 7-card hands
are possible in this game? Show your work.
7. A volleyball squad has twelve players.
a. How many ways can the players line up to greet the opposing team? Show your work.
b. There are 4 seniors on the team. What is the probability that a team of 6 players chosen randomly has all
the seniors on it? You must show how to set up this problem but you can use the short-cut key to
evaluate the answer.
8. How many license plates are possible using two letters followed by three digits, followed by one letter?
Show your work.
9. What is the probability that a randomly generated license plate code described in the question above starts and
ends with A,E,U, or Y? Show work.
10. Seven African American, 5 Asian, 6 Hispanic and 5 Caucasian students are finalists to participate in a
summer enrichment camp. From these students, 6 winners will be selected randomly. What’s the
probability there will be no Hispanics among the winners? If his occurs, will you suspect discrimination?
Explain.
11. A committee of five members is to be randomly selected from a group of nine freshmen and seven
sophomores. You can use the short cut key on your calculator but show what you entered.
a. How many different committees of three freshman and two sophomores can be chosen?
b. What is the probability that Jake, a freshman, is on a randomly chosen committee?
12. There are 11 boys and 18 girls in a chemistry class. Show your work.
a. How many ways can one boy and one girl be chosen to run an errand for the teacher?
c. How many ways can one boy or one girl be chosen?
13. How many ways can the letters in the following words be arranged? Show your work.
a. COUNT
b. SIGNIFICANT
14. Thinking about 5-card poker hands…
a. How many hands are possible? You can use the short-cut key, but show the set-up.
c.
How many hands with exactly 2 Aces are possible?
d. How many hands are possible with exactly 2 or 3 Aces?
15. Passwords for a cell phone use two letters followed by two digits followed by a special symbol (@, #, $, %,
or &). Show your work.
a. How many different passwords are possible?
b. What’s the probability that a password generated randomly will contain your first and last name
initials, in order?
16. After an unusually dry autumn, a radio announcer is heard to say, “Watch, out! We’ll pay for these sunny
days later on this winter.” Explain what the radio announce is trying to say, and comment on the validity of
his reasoning.
17. Evaluate each of the following without using the “!” button on your calculator. Show your work.
A. 5!
D.
88!
87!1!
B.
14!
10!
C.
52!
50!
E.
13!
11!2!
F. 0!
18. Show how to use the formulas to set up and simplify each problem. You may then use your calculator
to evaluate the result.
A.
12C8
D. 8P8
B. 9P5
C. 8C8
E. 5C0
F. 5P0
MULTIPLE CHOICE
18. A casino claims that its roulette wheel is truly random. What should that claim mean?
a. Every number is equally likely to occur.
b. The probabilities of all numbers will add to 1.
c. The same number will not come up twice in a row.
d. Every number will occur before any numbers repeat.
19.
A doctor tells a patient that there’s a 70% chance they will live at least 10 years. Where do you think that
probability came from?
a. This estimate is based on the patient’s current health.
b. This estimate is based on computer simulation.
c. This estimate is based on the long-run experience for similar patients.
d. This estimate is based on the doctor’s experience with the disease.
20. Commercial airplanes have an excellent safety record. Nevertheless, there are accidents occasionally, with
the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of
passengers, probably because people are afraid to risk flying. A travel agent suggests that since the “Law of
Averages” makes it highly unlikely to have two plane crashes within a few weeks of each other, flying soon
after a crash is the safest time to fly. What do you think? Explain.
a. This statement is false because the “Law of Averages” does not exist and each crash is independent
of one another.
b. This statement is false because this is the incorrect understanding of the “Law of Averages.” What
the travel agent is describing is the “Law of Large Numbers.”
c. This statement if true because each crash is dependent on one another.
d. This statement if true because each crash is dependent on one another.
21. A city recently held interviews for 5 jobs available. Even though there were 12 Republicans among the 24
applicants, none of them were hired. Noting that the mayor is a Democrat, the local Republican Party
chairperson has challenged the fairness of what was supposed to be a non-political process. What do you
think? Assuming that the qualifications of the applicants don’t depend on their political affiliation, is it
reasonable to believe that this outcome could simply have happened by chance?
A. Find the probability that no Republicans were hired.
B. Is it reasonable to believe that this outcome could simply have happened by chance?
a. Yes, because it would not be unusual to hire no Republicans, if they were really randomly
selected for the job.
b. No, because it would be unusual to hire no Republicans, if they were really randomly
selected for the job.
c. Yes, the probability is not low. Each person had an equal chance of being hired.
d. No, the probability is low enough. Therefore, it is possible that all Democrats were
randomly selected.
22. A family has 4 children, which of the following is the sample space for the number of girls?
a. S={1, 2, 3}
b. S={1, 2, 3, 4}
c. S={0, 1, 2, 3}
d. S={0, 1, 2, 3, 4}
23. Are the outcomes in the problem above equally likely to occur?
a. no
b. yes
24. Create an appropriate sample space for a family that has four children and use it to calculate the probability
of having exactly three girls.