Review Questions
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C HAPTER
Chapter 1. Review Questions
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Review Questions
Answer the following questions and show all work (including diagrams) to create a complete answer. 1. Match the following statements from the first column with the probability values in the second column.
TABLE 1.1: Probability Statement a. The probability of this event will never occur. b. The probability of this event is highly likely. c. The probability of this event is very likely. d. The probability of this event is somewhat likely. e. The probability of this event is certain.
P(X) P(X) = 1.0 P(X) = 0.33 P(X) = 0.67 P(X) = 0.00 P(X) = 0.95
2. Match the following statements from the first column with the probability values in the second column.
TABLE 1.2: Probability Statement a. I bought a ticket for the State Lottery. The probability of a successful event (winning) is likely to be: b. I have a bag of equal numbers of red and green jelly beans. The probability of reaching into the bag and picking out a red jelly bean is likely to be: c. My dad teaches math, and my mom teaches chemistry. The probability that I will be expected to study science or math is likely to be: d. Our class has the highest test scores in the State Math Exams. The probability that I have scored a great mark is likely to be: e. The Chicago baseball team has won every game this season. The probability that the team will make it to the playoffs is likely to be:
P(X) P(X) = 0.80 P(X) = 0.50
P(X) = 0.67
P(X) = 1.0
P(X) = 0.01
3. Read each of the following statements and match the following words to each statement. You can put your answers directly into the table. Here is the list of terms you can add: • • • • • •
certain or sure impossible likely or probable unlikely or improbable maybe uncertain or unsure
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TABLE 1.3: Statement Tomorrow is Friday. I will be in New York on Friday. It will be dark tonight. It is snowing in August! China is cold in January.
Probability Term
4. Read each of the following statements and match the following words to each statement. You can put your answers directly into the table. Here is the list of terms you can add: • • • • • •
certain or sure impossible likely or probable unlikely or improbable maybe uncertain or unsure
TABLE 1.4: Statement I am having a sandwich for lunch. I have school tomorrow. I will go to the movies tonight. January is warm in New York. My dog will bark.
Probability Term
5. The probability of scoring at least an 80% on a math test is 20%. What is the probability of scoring below 80%? 6. The probability of getting a job after university is 85%. What is the probability of not getting a job after university? 7. Does the following table represent the probability distribution for a discrete random variable? X
2
4
6
8
P(X)
0.2
0.4
0.6
0.8
8. Does the following table represent the probability distribution for a discrete random variable? X
1
2
3
4
5
P(X)
0.202
0.174
0.096
0.078
0.055
9. Does the following table represent the probability distribution for a discrete random variable? X
1
2
3
4
5
6
P(X)
0.302
0.251
0.174
0.109
0.097
0.067
10. A fair die is rolled 10 times. Let X be the number of rolls in which we see a 6. a. What is the probability of seeing a 6 in any one of the rolls? b. What is the probability that we will see a 6 exactly once in the 10 rolls? 11. A fair die is rolled 15 times. Let X be the number of rolls in which we see a 6. 2
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Chapter 1. Review Questions
a. What is the probability of seeing a 6 in any one of the rolls? b. What is the probability that we will see a 6 exactly once in the 15 rolls? 12. A fair die is rolled 15 times. Let X be the number of rolls in which we see a 5. a. What is the probability of seeing a 5 in any one of the rolls? b. What is the probability that we will see a 5 exactly 7 times in the 15 rolls? 13. A pair of fair dice is rolled 10 times. Let X be the number of rolls in which we see at least one 5. a. What is the probability of seeing at least one 5 in any one roll of the pair of dice? b. What is the probability that in exactly half of the 10 rolls, we see at least one 5? 14. A pair of fair dice is rolled 15 times. Let X be the number of rolls in which we see at least one 5. a. What is the probability of seeing at least one 5 in any one roll of the pair of dice? b. What is the probability that in exactly 8 of the 15 rolls, we see at least one 5? 15. You are randomly drawing cards from an ordinary deck of cards. Every time you pick one, you place it back in the deck. You do this 9 times. What is the probability of drawing 2 hearts, 2 spades, 2 clubs, and 3 diamonds? 16. A telephone survey measured the percentage of students in ABC town who watch channels NBX, FIX, MMA, and TSA, respectively. After the survey, analysis showed that 35% watch channel NBX, 40% watch channel FIX, 10% watch channel MMA, and 15% watch channel TSA. What is the probability that from 8 randomly selected students, 1 will be watching channel NBX, 2 will be watching channel FIX, 3 will be watching channel MMA, and 2 will be watching channel TSA? 17. Based on what you know about probabilities, write definitions for theoretical and experimental probability. 18. Based on what you have learned, answer the following questions. a. What is the difference between theoretical and experimental probability? b. As you add more data, do your experimental probabilities get closer to or further away from your theoretical probabilities? c. Is tossing 1 coin 100 times the same as tossing 100 coins 1 time? Why or why not? 19. Use the randBin function on your calculator to simulate tossing 5 coins 25 times to determine the probability of getting 2 tails. 20. Use the randBin function on your calculator to simulate tossing 10 coins 50 times to determine the probability of getting 4 heads. 21. Calculate the theoretical probability of getting 3 heads in 10 tosses of a coin. 22. Find the experimental probability using technology of getting 3 heads in 10 tosses of 3 coins. 23. Calculate the theoretical probability of getting 8 heads in 12 tosses of a coin. 24. Calculate the theoretical probability of getting 7 heads in 14 tosses of a coin.
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