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1 5_2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A prix fixed menu offers a choice of 2 appetizers, 4 main courses and 3 desserts. If a tree diagram is used to list all possible meal combinations from the prix fixed menu, how many branches will there be? A) none of these B) 12 C) 8 D) 24 E) 9 2) The General Social Survey asked subjects whether they favored or opposed the death penalty for persons convicted of murder (F = favor, O = oppose) and whether they favored or opposed a law which would require a person to obtain a permit before he or she could buy a gun (1 = favor, 2 = oppose) as well as if they had ever been married (Y = yes, N = no). If a tree diagram is used to list the sample space with the first branch representing the response to the death penalty question, the second the response to the gun permit question and the third the response to the marriage question, which of the following is a possible outcome? A) N2F B) F1Y C) FOY D) 1ON E) OON 3) Suppose the following tree diagram summarizes the responses of 500 people to two questions, where the first response is either yes or no and the second is multiple choice with three possible answers (A, B or C). Use the tree diagram to calculate the probability that a person answered YB (yes, B). 1) 2) 3) A) 0.7 B) 0.4 C) 0.07 D) 0.04 E) 0.5 1

2 4) Suppose the following tree diagram summarizes the responses of 500 people to two questions, where the first response is either yes or no and the second is multiple choice with three possible answers (A, B or C). Use the tree diagram to calculate the probability that a person answered B to the multiple choice question. 4) A) 0.7 B) 0.04 C) 0.07 D) 0.4 E) ) A sample of two light bulbs is selected in succession, without replacement, from among 6 good ones and 4 defective ones. List the probabilities corresponding to the four branches (GG, GD, DG, DD). 5) A) 0.3, 0.24, 0.24, 0.12 B) 0.36, 0.24, 0.24, 0.16 C) 0.33, 0.27, 0.27, 0.13 D) 0.33, 0.24, 0.24, ) A sample of two light bulbs is selected in succession, without replacement, from among 6 good ones and 4 defective ones. Is the trial of selecting the first light bulb independent of the trial of selecting the second light bulb? A) No B) Yes 7) A sample of two light bulbs is selected in succession, without replacement, from among 6 good ones and 4 defective ones. What is the complement of the event "at least one light bulb is defective"? A) both bulbs are defective B) at least one bulb is not defective C) neither bulb is defective 6) 7) 2

3 8) A sample of two light bulbs is selected in succession, without replacement, from among 6 good ones and 4 defective ones. What is the probability of obtaining at least one defective bulb? 8) A) 0.64 B) 0.67 C) 0.4 D) 0.7 E) ) A student is taking two pass/fail courses over the summer break. What is the sample space for the student's grades? A) {P, F} B) {P, P, F, F} C) {PP, PF, FP, FF} D) {PP, PF, FF} 9) List the outcomes comprising the specified event. 10) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. 10) ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. List the outcomes that comprise the event that Charlie is selected. A) ABC, ACD, ACE, BCD, BCE, B) CDE C) ABC, ACD, ACE, BCD, BCE, CDE D) ABC, ACD, ACE, BCD, BCE, CDE, BDE E) ABC, ACD, ACE, BCD, CDE 3

4 11) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. 11) ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. List the outcomes that comprise the event that Betty and Emily are selected. A) ABE, BCE B) ABE, BCE, BDE C) ABC, ABD, ABE, ACE, ADE, BCD, BCE, BDE, CDE D) ABE, BDE E) BE 12) When a quarter is tossed four times, 16 outcomes are possible. 12) HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the event of tossing exactly three tails. A) TTTH B) HTTT, THTT, TTHT, TTTH C) HTTT, THTT, TTHT, TTTH, TTTT D) THTT, TTHT, TTTH E) HTTT, THTT, TTTH 13) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Bob, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. 13) ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be on the board. Let A = event that Bob and Dave are both selected. List the outcomes that comprise the complement of A, AC. A) ABD, BCD, BDE B) ABC, ABE, ACD, ACE, ADE, BCE, CDE C) ABC, ABE, ACD, ACE, ADE D) ACE E) ABC, ABE, ACE, ADE, BCE, CDE 4

5 Determine whether the events are disjoint. 14) When a quarter is tossed four times, 16 outcomes are possible. 14) HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The events A and B are defined as follows. A = event the first two tosses are heads B = event the first and last tosses are the same Are the events A and B disjoint? A) No B) Yes 15) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. 15) ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. The events A and B are defined as follows. A = event that Betty and Allison are both selected B = event that more than one man is selected Are the events A and B disjoint? A) No B) Yes 16) A card is selected randomly from a deck of 52. The events A, B, and C are defined as follows. 16) A = event the card selected is a heart B = event the card selected is a club C = event the card selected is an ace Are the events A, B, and C disjoint? A) No B) Yes 5

6 17) The age distribution of students at a community college is given below. 17) Age (years) Number of students (f) Under Over A student from the community college is selected at random. The events A, B, and C are defined as follows. A = event the student is at most 28 B = event the student is at least 40 C = event the student is between 21 and 24 inclusive Are the events A, B, and C disjoint? A) No B) Yes Draw a Venn diagram and shade the described events. 18) From a finite sample, events A, B, and C are disjoint. Shade the collection A or B or C. 18) A) B) C) 6

7 D) E) 19) From a finite sample, events A and B are not disjoint; however, event C is disjoint from events A and B. Shade the collection (A and B) or C. A) 19) B) C) 7

8 D) E) Suppose P(C) =0.048, P(M and C) = 0.044, and P(M or C) = Find the indicated probability. 20) P(M) 20) A) B) C) D) E) ) P[(M and C)c] 21) A) B) C) 0 D) E) ) P(Mc and Cc) 22) A) B) C) D) 0 E) Find the indicated probability. 23) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT. What is the probability of getting at least one head? 23) A) 1 8 B) 7 8 C) 1 2 D) 1 4 E) ) If two balanced die are rolled, the possible outcomes can be represented as follows. 24) (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 7. A) B) C) D) 7 18 E) 1 6 8

9 25) A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. 25) (Hint: There are 10 possible samples.) 7 A) B) C) 1 5 D) 1 2 E) 3 5 Find the probability using complements. 26) A percentage distribution is given below for the size of families in one U.S. city. 26) Size Percentage A family is selected at random. Find the probability that the size of the family is 4 or more. Round your result to three decimal places. A) B) C) D) E) ) When a coin is tossed two times, the possible outcomes are HH HT TH TT where H represents a head and T represents a tail. What is the probability of AC where A = the event of tossing at least one head? A) 0.75 B) 0.50 C) D) 0.25 E) 1 28) A greenhouse is offering a sale on tulip bulbs because they have inadvertently mixed pink bulbs with red bulbs. If 40% of the bulbs are pink and 60% are red, what is the probability that at least one of the bulbs will be pink if 4 bulbs are purchased? A) B) C) 1 D) E) ) 28) Find the probability of the given event. 29) A single fair die is rolled. The number on the die is a 3 or a 5. 29) A) 1 B) 1 C) 1 1 D) 2 E) ) Two fair dice are rolled. The sum of the numbers on the dice is 1 or 5. 30) A) B) C) 0 D) E) ) A lottery game has balls numbered 1 through 15. A randomly selected ball has an even number or a 6. 3 A) B) C) 7 D) E) ) 9

10 32) A random spinner has equal-sized regions numbered 1 through 18. The spinner stops on an even number or a multiple of 3. 32) A) 15 B) 1 2 C) 1 D) 1 3 E) 2 3 Find the indicated probability. 33) In 2006, 88.2% of respondents to the General Social Survey answered yes when asked if it should be possible for a pregnant woman to obtain a legal abortion if the woman s own health was seriously endangered by the pregnancy and 91.4% answered yes when asked whether they were in favor of sex education in public schools. If 82.6% of the respondents answered yes to both questions, what is the probability that a randomly selected respondent answered yes to at least one of the questions? A) B) 1 C) D) E) ) A survey of senior citizens at a doctor's office shows that 52% take blood pressure-lowering medication, 43% take cholesterol-lowering medication, and 5% take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication? A) 1 B) 0.85 C) 0.90 D) 0.14 E) 0 35) The probability that a student at a certain college is male is The probability that a student at that college has a job off campus is The probability that a student at the college is male and has a job off campus is If a student is chosen at random from the college, what is the probability that the student is male or has an off campus job? A) 0.37 B) 0.63 C) 0.78 D) 0.93 E) ) At a California college, 22% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks Spanish but not French? A) 0.17 B) 0.02 C) 0.19 D) 0.81 E) ) 34) 35) 36) Select the most appropriate answer. 37) For two events A and B, P(A) = 0.8, P(B) = 0.2, and P(A and B) = It follows that A and B are 37) A) disjoint but not independent. B) neither disjoint nor independent. C) independent but not disjoint. D) both disjoint and independent. E) complementary. 38) For two events A and B, P(A) = 0.4 and P(B) = 0.5. Then P(A or B) equals 38) A) 0.9, if A and B are independent. B) 0.7, if A and B are disjoint.. C) 0.7, if A and B are independent. D) 0, if A and B are disjoint. E) 0.2, if A and B are independent. 10

11 Answer Key Testname: 5_2 1) D 2) B 3) D 4) E 5) C 6) A 7) C 8) B 9) C 10) C 11) B 12) B 13) B 14) A 15) B 16) A 17) A 18) B 19) E 20) E 21) E 22) A 23) B 24) E 25) E 26) D 27) D 28) A 29) B 30) A 31) E 32) E 33) E 34) C 35) B 36) C 37) C 38) C 11

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