Study Guide - Probability and Counting Rules

  • 格式:rtf
  • 大小:344.09 KB
  • 文档页数:11

Study Guide - Probability and Counting Rules1. What is the set of all possible outcomes of a probability experiment?A) outcomeB) sample spaceC) eventsD) Venn diagrams2. How many possible outcomes would there be if three coins were tossed once?A) 2B) 4C) 6D) 83. What type of probability uses sample spaces to determine the numerical probability that an event willoccur?A) classical probabilityB) conditional probabilityC) empirical probabilityD) subjective probability4. If a sportscaster makes an educated guess as to how well a team will do this season, he is using whattype of probability?A) classical probabilityB) conditional probabilityC) empirical probabilityD) subjective probability5. The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50factory workers. If a person is selected at random, what is the probability that he or she is a factoryworker?A) 14B) 18C) 58D) 256. If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a diamond?A) 12B) 13C) 14D) 157. A compound event consists of two or more outcomes or simple events.A) TrueB) False8. Classical probability was the first type of probability studied formally by mathematicians.A) TrueB) False9. A child gets 22 heads out of 30 tosses of a coin. This would be an example of ____________ type ofprobability.10. If one tosses a coin enough times, the number of heads and tails will tend to “even out.” This is anexample of the ______________.11. If a die were rolled, the event of getting an even number would be called a simple event.A) TrueB) False12. What are the odds against drawing a card from an ordinary deck of cards and getting a spade?13. In a recent study, the following data was obtained in response to the question, “Do you favor recyclingin your neighborhood?”Yes No No OpinionMales 25 15 10Females 30 10 10If a person is picked at random, what is the probability that the person is either male or has no opinion regarding recycling?A) 35B) 310C) 45D) 71014. Two events are mutually exclusive if they cannot occur at the same time.A) TrueB) False15. A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected atrandom, the probability that it is white or black would be 2 3.A) TrueB) False16. Given the following Venn diagram, which of the following equations would be used to calculate theprobability of either event A , event B , or event C occurring.A)P A B C P A P B P C P A B P B C ()()()()()()or or and and =++--B)P A B C P A P B P C P A B P A C P B C P A B C ()()()()()()()() or or and and and and and =+++++-C)P A B C P A P B P C P A B C ()()()()() or or and and =++- D) P A B C P A P B P C ()()()() or or =++17. If a single card is drawn from an ordinary deck of cards, what is the probability of drawing either aheart or a 6? A) 1752 B) 413 C) 926 D) 51318. If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace,a king of hearts, or a spade? A) 1952 B) 926 C) 1752 D) 112619. When the outcome or occurrence of the first event does not affect the outcome or occurrence of thesecond event in such a way that the probability is changed, the events are said to be dependent.A) TrueB) False20. Two events A and B are ______________ if the fact that A occurs does not affect the probability of Boccurring.21. When two events are independent, the probability of both occurring is:A) P A B P A P Band =⋅()()()B) P A B P A P Band =+()()()C) P A B P A Band =⋅()()D) P A B P A Band =+()()22. A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemonflavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?A) 0.0264B) 0.0531C) 0.0347D) 0.048223. A recent poll by the American Automobile Club found that 30% of those surveyed are worried aboutaggressive drivers on the road. If three people are selected at random, what is the probability that all three will be worried about aggressive drivers on the road?A) 0.900B) 0.027C) 0.081D) 0.30024. If a coin were tossed three times, the probability that the coin will land on heads at least one of thosethree times would be 7/8.A) TrueB) False25. If a card is drawn from an ordinary deck of cards, not replaced and then a second card is drawn fromthe same deck, these two events are ________________.26. The ______________ probability of an event B in relationship to an event A is defined as theprobability that event B occurs after event A has already occurred.27. It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. Ifthe speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph?28. On an eight question true-false quiz, a student guesses each answer. What is the probability that he/shegets at least one of the answers correct?29. Given eight students, three of which are females, if two students are selected at random, withoutreplacement, what is the probability that both students are female?30. A box contains blue chips and red chips. A person selects two chips without replacement. If theprobability of selecting a blue chip and a red chip is 32128, and the probability of selecting a blue chipon the first draw is516, find the probability of selecting the red chip on the second draw, given thatthe first chip selected was a blue chip.A) 15B) 25C) 35D) 4531. The number of different arrangements of four pictures from a selection of ten pictures is 5,040.A) TrueB) False32. The __________ rule is the number of ways that r objects can be selected from n objects when order isnot important.33. How many times was the coin tossed in the figure below?A) 3B) 6C) 4D) 234. Box A contains the numbers 1, 2, 3, and 4. Box B contains the numbers 5, 6, 7, and 8. A number is firstdrawn from Box A and then another number from Box B. Using Figure 4–2, how many outcomes are possible if both numbers are even?A) 16B) 4C) 6D) 835. When drawing cards from a box, if the selected card is replaced, then repetitions are not allowed.A) TrueB) False36. Evaluate the following: 7P3.A) 210B) 35C) 5,040D) 637. A business has seven locations to choose from and wishes to rank only the top three locations. Howmany different ways can this be done?A) 5,040B) 210C) 840D) 42038. Evaluate the following: 7C3.A) 210B) 5,040C) 35D) 639. A club has 10 members. There are 1,260 ways that a chairperson, a secretary, and a treasurer can beselected from these 10 members.A) TrueB) False40. There are 2,368 possible ways that a committee of eight people can be selected from a group of 14people.A) TrueB) False41. There are __________ possible ways that eight pictures can be hung on a wall.42. If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes arepossible if repetitions are not permitted?A) 625B) 720C) 7,776D) 1,29643. When a die is rolled twice, there are __________ outcomes.44. How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera ifAndy and Betty must sit together?A) 24B) 12C) 6D) 1845. In how many ways can a student select five questions from an exam containing 12 questions if he mustanswer the last question?A) 330B) 7920C) 40,320D) 95,04046. There are four instructors, nine assistant professors, and five associate professors in the Mathdepartment. A committee of five is selected to choose new textbooks. There are 1,440 ways that a committee can be selected, if there must be one instructor, two assistant professors, and two associate professors on the committee.A) TrueB) False47. A small school bus contains eight first-graders and ten second-graders. If two children are ill, what isthe probability that at least one of them is a second-grader?A) 28153B) 125153C) 16153D) 2730648. If five cards are drawn from a deck of cards without replacement, what is the probability that at leastone of the cards is a heart?Answer Key1. B2. D3. A4. D5. C6. A7. A8. A9. empirical10. law of large numbers11. B12.3:1, 75%, 0.75, or 3 413. A14. A15. A16. A17. B18. C19. B20. independent21. A22. C23. B24. A25. dependent26. conditional27. 0.1128. 25525629. 32830. D31. A32. combination33. D34. B35. B36. A37. B38. C39. B40. B41. 40,32042. B43. 3644. B45. A46. A47. B48. 74119520Page 11。