Ch. 6 Review. AP Statistics

Transcription

1 Ch. 6 Review AP Statistics 1. The probability of any outcome of a random phenomenon is A) the precise degree of randomness present in the phenomenon. B) any number as long as it is between 0 and 1. C) either 0 or 1, depending on whether or not the phenomenon can actually occur or not. D) the proportion of a very long series of repetitions on which the outcome occurs. E) none of these. 2. A randomly selected student is asked to respond Yes, No, or Maybe to the question Do you intend to vote in the next presidential election? The sample space is {Yes, No, Maybe}. Which of the following represents a legitimate assignment of probabilities for this sample space? A) 0.4, 0.4, 0.2 D) 0.5, 0.3, 0.2 B) 0.4, 0.6, 0.4 E) none of these C) 0.3, 0.3, If you choose a card at random from a well-shuffled deck of 52 cards, what is the probability that the card is not a heart? A) 0.25 B) 0.5 C) 0.75 D) 1 E) none of these 4. You play tennis regularly with a friend, and from past experience, you believe that the outcome of each match is independent. For any given match you have probability 0.6 of winning. The probability that you win the next two matches is A) 0.16 B) 0.36 C) 0.4 D) 0.6 E) If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)? A) B) 0.28 C) D) 0.76 E) the answer cannot be determined from the information given. 6. If P(A) = 0.3 and P(B) = 0.75 and A and B are independent, what is P(A and B)? A) B) 0.75 C) D) 0.3 E) Suppose we roll a red die and a green die. Let A be the event that the number of spots showing on the red die is 4 or less and B be the event that the number of spots showing on the green die is more than 2. The events A and B are A) disjoint. B) independent. C) dependent. D) reciprocals. E) complements. 8. In a table of random digits such as Table B, each digit is equally likely to be any of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. What is the probability that a digit in the table is a 0? A) 1 B) 0 C) 1/9 D) 9/10 E) 1/10

2 9. In a table of random digits such as Table B, each digit is equally likely to be any of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. What is the probability that a digit in the table is 7 or greater? A) 1/3 B) 1/5 C) 3/10 D) 2/5 E) 7/ Choose an American household at random and let X be the number of cars (including SUVs and light trucks) they own. Here is the probability model if we ignore the few households that own more than 5 cars: X P(X) A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold? A) 7% D) 45% B) 13% E) 55% C) 20% 11. Choose a student at random and give him or her an IQ test. The score X follows the N(100, 15) distribution. The probability P(X > 120) that the person chosen has an IQ score higher than 120 is about A) B) C) D) E) You can t say for sure, but the student is very unlikely to score higher than Two dice are rolled. The probability of getting a sum greater than 9 is A) 1/9 B) 1/6 C) 1/3 D) 1/2 E) about A coin is tossed 5 times. Find the probability of getting at least one tail. Hint: The probability of getting at least one tail is the complement of P(all 5 flips were heads). A) 1/32 B) 1/4 C) 1/3 D) 1/2 E) 31/ Two dice are rolled. Find the probability of getting a sum less than 4 or greater than 9. A) 1/6 B) 1/4 C) 1/3 D) 1/2 E) about Which of the following pairs of events are disjoint (mutually exclusive)? A) A: the odd numbers; B: the number 5 B) A: the even numbers; B: the numbers greater than 10 C) A: the numbers less than 5; B: all negative numbers D) A: the numbers above 100; B: the numbers less than 200 E) A: negative numbers; B: odd numbers

3 16. Students at University X must have one of four class ranks freshman, sophomore, junior, or senior. At University X, 35% of the students are freshmen and 21% are sophomores. If a University X student is selected at random, the probability that he or she is either a junior or a senior is A) 56 B) 1 or 0 C) 0.66 D) 0.56 E) People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O- negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor? A) D) 0 B) 0.72 E) 1 C) If A U B = S (sample space), P(A and B c ) = 0.25, and P(A c ) = 0.35, then P(B) = A) 0.35 D) 0.75 B) 0.4 E) none of these. C) If a peanut M&M is chosen at random, the chances of it being a particular color are shown in the table below. Color Brown Red Yellow Green Orange Blue Probability ? According to the table, the probability of randomly drawing a blue peanut M&M is A) 1 D) 0.1 B) 0.3 E) 0 C) 0.2 Use the following to answer questions 20 to 23: Government data give the following counts of violent deaths in a recent year among people 20 to 24 years of age by sex and cause of death: Female Male Accidents Homicide Suicide Choose a violent death in this age group at random. The probability that the victim was male is A) 0.81 B) 0.78 C) 0.59 D) 0.46 E) 0.19

4 21. The conditional probability that the victim was male, given that the death was accidental, is about A) 0.46 B) 0.48 C) 0.56 D) 0.78 E) The conditional probability that the death was accidental, given that the victim was male, is about A) 0.81 B) 0.56 C) 0.78 D) 0.48 E) Let A be the event that a victim of violent death was a woman and B the event that the death was a suicide. The proportion of suicides among violent deaths of women is expressed in probability notation as A) B) C) P(A and B) D) P(A B) E) P(B A) 24. The chances that you will be ticketed for illegal parking on any given day on campus are about 1/3. During the last nine days, you have illegally parked every day and have NOT been ticketed (you lucky person!). Today, on the 10 th day, you again decide to park illegally. The chances that you will be caught are A) greater than 1/3 because you were not caught in the last nine days. B) less than 1/3 because you were not caught in the last nine days. C) still equal to 1/3 because the last nine days do not affect the probability. D) equal to 1/10 because you were not caught in the last nine days. E) equal to 9/10 because you were not caught in the last nine days. 25. Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3. P(A B) is A) 0.09 B) 0.51 C) 0.52 D) 0.57 E) Suppose that A and B are two independent events with P(A) = 0.2 and P(B) = 0.4. P(A B C ) is A) 0.08 B) 0.12 C) 0.52 D) 0.6 E) In a certain town 60% of the households own a cellular phone, 40% own a pager, and 20% own both a cellular phone and a pager. The proportion of households that own a cellular phone but not a pager is A) 20% B) 30% C) 40% D) 50% E) 80%

5 Use the following to answer questions 28 through 31: A system has two components that operate in parallel, as shown in the diagram below. Since the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probabilities of failures for the components 1 and 2 during one period of operation are.20 and.03, respectively. Let F denote the event that component 1 fails during one period of operation and G denote the event that component 2 fails during one period of operation. Component failures are independent. 28. The probability that the system functions properly during one period of operation is A) B) C) D) E) The event corresponding to the system functioning properly during one period of operation is A) F G B) (F G) c C) F c G c D) F G 30. The event corresponding to the system failing during one period of operation is A) F G B) F G C) (F G) c D) F c G c 31. The probability that the system fails during one period of operation is A) B) C) D) E) Use the following to answer questions 32-33: An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is Referring to the information above, the conditional probability of A given B A) is 0.3 B) is 0.2 C) is 1/6 D) is 0.1 E) cannot be determined from the information given. 33. Referring to the information above, we may conclude A) that events A and B are independent. D) that events A and B are disjoint. B) that events A and B are complements. E) none of the above. C) that either A or B always occurs.

6 34. Let P(A) = 0.3 and P(B Α) = 1/6. What is the conditional probability that B occurs given that A occurs? A) 1 B) 9/5 C) 4/9 D) 5/9 E) This cannot be determined from the information given. 35. Event A occurs with probability 0.8. The conditional probability that event B occurs given that A occurs is 0.5. The probability that both A and B occur A) is 0.3 B) is 0.4 C) is 0.5 D) is 0.8 E) cannot be determined from the information given. 36. Event A occurs with probability 0.3 and event B occurs with probability 0.4. If A and B are independent, we may conclude that A) P(A and B) = 0.12 D) P(A or B) = 0.58 B) P(A B) = 0.3 E) all of the above. C) P(B A) = An assignment of probabilities must obey which of the following? A) The probability of any event must be a number between 0 and 1, inclusive. B) The sum of the probabilities of all outcomes in the sample space must be exactly 1. C) The probability of an event is the sum of the outcomes in the sample space that make up the event. D) All of the above. E) Only A and B are true. 38. Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then A) P(A and B) = 0.16 B) P(A or B) = 1 C) P(A and B) = 1 D) P(A or B) = 0.16 E) Both A and B are true. 39. A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear for these 1996 additional tosses? A) 996 B) 998 C) 1000 D) 1996 E) none of these.

7 40. A die is loaded so that the number 6 comes up three times as often as any other number. What is the probability of rolling a 1 or 6? A) 1/3 B) ¼ C) ½ D) 2/3 E) none of these. 41. Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10% of the time when a person is telling the truth and 95% of the time when the person is lying. Suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent one-person crime. Then the probability of observing no positive reading if all suspects plead innocent and are telling the truth is A) B) C) D) E) If you buy one ticket in the Provincial Lottery, then the probability that you will win a prize is If you buy one ticket each month for five months, what is the probability that you will win at least one prize? A) 0.55 B) 0.5 C) 0.44 D) 0.45 E) An instant lottery game gives you probability 0.02 of winning on any one play. Plays are independent of each other. If you play 3 times, the probability that you win on none of your plays is about A) 0.98 B) 0.94 C) D) 0.06 E) The probability that you win one or more of your 3 plays of the game in the previous question is about A) 0.06 B) 0.02 C) D) 0.04 E) Choose an American adult at random. The probability that you chose a woman is The probability that the person you choose has never married is The probability that you choose a woman who has never married is The probability that the person you choose is either a woman or never married (or both) is therefore bout A) 0.76 B) 0.65 C) 0.12 D) 0.87 E) Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2 % were Asian. (This ignores a small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The probability that a randomly chosen death is a white who died of diabetes is about A) B) C) D) 0.86 E) Using the information in the previous question, the probability that a randomly chosen death was due to diabetes is about A) B) C) D) 0.96 E) 0.030

8 Ch 6 Review Answers 1. D 2. A 3. C 4. B 5. C 6. C 7. B 8. E 9. C 10. C 11. D 12. B 13. E 14. B 15. D 16. E 17. A 18. D 19. E 20. A 21. D 22. B 23. E 24. C 25. B 26. B 27. C 28. A 29. C 30. A 31. E 32. C 33. C 34. D 35. B 36. E 37. D 38. B 39. B 40. C 41. D 42. C 43. B 44. A 45. B 46. C 47. E