Exercise Set 6.3: Rules of Probability 1. If a fair die is tossed once, find the probability that the uppermost face displays a(n): 5. and P ( E F ) = 0.19 . Find the following: A. 2 or a 6 A. P ( E F ) D. P ( E c ) B. odd number or a 5 B. P ( E F c ) E. P ( F c ) C. odd number or a 4 C. P ( E c F ) F. P ( E F ) D. 8 or an odd number E. even number or a multiple of 3 2. Suppose that P ( E ) = 0.74 , P ( F ) = 0.33 , 6. c Suppose that P ( E ) = 0.61 , P ( F ) = 0.43 , If a fair die is tossed once, find the probability that the uppermost face displays a(n): and P ( E F ) = 0.27 . Find the following: A. P ( E F ) D. P ( E c ) A. 5 or an even number B. P ( E F c ) E. P ( F c ) B. 1 or a 3 C. P ( E c F ) F. P ( E F ) c C. even number or a 2 D. odd number or a factor of 10 3. 7. and P ( E F ) = 0.37 . Find the following: Suppose that you draw one card from a well-shuffled deck of 52 playing cards. Find the probability that the drawn card is a(n): A. P ( E F ) D. P ( E c ) B. P ( E F c ) E. P ( F c ) C. P ( E c F ) F. P ( E F ) A. red 10 or a spade B. 8 or a club C. red card or a face card 8. E. black card or a King Suppose that you draw one card from a well-shuffled deck of 52 playing cards. Find the probability that the drawn card is a(n): A. Queen or a diamond B. 3 or a King c Suppose that P ( E ) = 0.73 , P ( F ) = 0.57 , and P ( E F ) = 0.41 . Find the following: D. diamond or a heart 4. Suppose that P ( E ) = 0.81 , P ( F ) = 0.54 , E. 10 or a 4 9. A. P ( E F ) D. P ( E c ) B. P ( E F c ) E. P ( F c ) C. P ( E c F ) F. P ( E F ) c Suppose that P ( E ) = 0.59 , P ( F ) = 0.48 , and P ( E F c ) = 0.27 . Find the following: C. black 10 or a club A. P ( E F ) D. P ( E c ) D. face card or a heart B. P ( E F ) E. P ( F c ) E. spade or a red card C. P ( E c F ) F. P ( E c F c ) 360 University of Houston Department of Mathematics Exercise Set 6.3: Rules of Probability 10. Suppose that P ( E ) = 0.74 , P ( F ) = 0.41 , and P ( E F c ) = 0.45. Find the following: 15. Suppose that P ( E ) = 0.27 , P ( F ) = 0.84 , and P ( E c F ) = 0.91 . Find the following: A. P ( E F ) D. P ( E c ) A. P ( E F ) E. P ( E F c ) B. P ( E F ) E. P ( F c ) B. P ( E F ) F. P ( E F c ) c C. P ( E c F ) F. P ( E c F c ) C. P ( E F c ) G. P ( E c F ) c D. P ( E c F ) H. P ( E c F c ) 11. Suppose that P ( E ) = 0.71 , P ( F ) = 0.53 , and P ( E c F ) = 0.15 . Find the following: A. P ( E F ) D. P ( E c ) B. P ( E F ) E. P ( F c ) C. P ( E F c ) F. P ( E c F c ) 16. Suppose that P ( E ) = 0.35 , P ( F ) = 0.67 , P ( E c F ) = 0.86 . Find the following: 12. Suppose that P ( E ) = 0.82 , P ( F ) = 0.63 , A. P ( E F ) D. P ( E c F ) B. P ( E F ) E. P ( E F c ) C. P ( E F c ) F. P ( E c F c ) and P ( E c F ) = 0.12 . Find the following: 17. Suppose that P ( E c ) = 0.53 , A. P ( E F ) D. P ( E c ) B. P ( E F ) E. P ( F c ) P ( E F ) = 0.28 , and P ( E c F ) = 0.20 . C. P ( E F c ) F. P ( E c F c ) Find the following: 13. Suppose that P ( E ) = 0.75 , P ( F ) = 0.53 , and P ( E F c ) = 0.81 . Find the following: A. P ( E F ) E. P ( E c F ) B. P ( E F ) F. P ( E F c ) c C. P ( E F c ) G. P ( E c F ) c D. P ( E c F ) H. P ( E c F c ) A. P ( E ) E. P ( E c F ) B. P ( F ) F. P ( E F c ) C. P ( E F ) G. P ( E c F c ) D. P ( E F c ) H. P ( E c F ) c 18. Suppose that P ( E c ) = 0.74 , P ( E F ) = 0.06 , and P ( E c F ) = 0.59 . Find the following: 14. Suppose that P ( E ) = 0.51 , P ( F ) = 0.73 , and P ( E F c ) = 0.60 . Find the following: A. P ( E F ) E. P ( E c F ) B. P ( E F ) F. P ( E F C. P ( E F c ) G. D. P ( E c F ) H. c ) P(E F ) P(E F ) c E. P ( E c F ) B. P ( F ) F. P ( E F c ) C. P ( E F ) G. P ( E c F c ) D. P ( E F c ) H. P ( E c F ) c c c c A. P ( E ) c MATH 1313 Finite Mathematics with Applications 361 Exercise Set 6.3: Rules of Probability 19. Suppose that P ( F c ) = 0.77 , P ( E F ) = 0.10 , and P ( E F c ) = 0.53 . Find the following: A. P ( E ) E. P ( E c F ) B. P ( F ) F. P ( E F c ) C. P ( E F ) G. P ( E c F c ) D. P ( E F ) H. P ( E F ) c c c 20. Suppose that P ( F c ) = 0.47 , P ( E F ) = 0.25 , and P ( E F c ) = 0.31 . 23. The Car Store surveyed 200 purchasers of new cars about the options they wanted on their new cars. Of the surveyed purchasers, 156 wanted a stereo system, 112 wanted a navigation system and 76 wanted both systems. Find the probability that a randomly selected new car purchaser wanted: A. Only 1 of the systems. B. Neither of the systems. C. A stereo system but not a navigation system. D. A navigation system but not a stereo system. Find the following: A. P ( E ) E. P ( E c F ) B. P ( F ) F. P ( E F c ) C. P ( E F ) G. P ( E c F c ) D. P ( E c F ) H. P ( E c F ) c 21. One hundred members of an organization were surveyed to see if they preferred meetings with speakers or social events. In response, 47 members preferred meetings with speakers, 68 preferred social events, and 28 wanted the organization to offer both. Find the probability that a randomly selected member: A. Prefers social events. B. Likes neither meetings with speakers nor social events. 22. Kava Koffee Klub surveyed 150 customers to determine how they take their coffee. Of the customers who were surveyed, 96 said they like sugar in their coffee, 76 like cream in their coffee, and 59 like both sugar and cream in their coffee. Find the probability that a randomly selected customer: A. Likes cream or sugar, but not both. B. Likes neither cream nor sugar. 362 24. Among 300 elementary school students, 258 said they like chocolate ice cream, 142 like vanilla ice cream and 102 like both. Find the probability that a randomly selected student likes: A. Vanilla ice cream or chocolate ice cream, but not both. B. Neither of the 2 flavors. C. Vanilla ice cream but not chocolate ice cream. D. Chocolate ice cream but not vanilla ice cream. 25. A group of UH students were surveyed about their math class enrollment this semester. Of the surveyed students, 116 were enrolled in Finite Math, 98 were enrolled in Business Calculus, 36 were enrolled in both and 17 were enrolled in neither. A. How many students were surveyed? Find the probability that a randomly selected student is enrolled in: B. Both Finite Math and Business Calculus. C. Exactly one of the math classes. D. Neither of the math classes. E. Finite Math but not Business Calculus. University of Houston Department of Mathematics Exercise Set 6.3: Rules of Probability 26. Some businessmen and businesswoman were surveyed about their appointment calendars. Of the surveyed business people, 139 said they keep their business appointments on an electronic calendar, 56 keep their appointments on a paper calendar, and 23 keep both a paper calendar and an electronic calendar. Three respondents do not keep a calendar. A. How many business professionals were surveyed? Find the probability that a randomly selected surveyed business professional: B. Keeps both an electronic and a paper calendar. C. Keeps only one type of calendar. D. Does not keep a calendar. E. Keeps an electronic calendar but not a paper calendar. 27. A cosmetic company offered special pricing on its skin care and make up products. The company surveyed its customers to track their purchases. The survey showed that 179 purchased skin care products, 145 purchased make up and 66 purchased both. A. How many customers were surveyed? Find the probability that a randomly selected customer purchased: B. Either skin care products or make up, but not both. C. Both skin care products and make up. D. Only skin care products. 28. A health club surveyed its members to determine if they worked out alone or with a personal trainer. The survey shows that 111 members work out alone, 67 work out with a personal trainer, and 41 sometimes work out alone and sometimes work out with a personal trainer. A. How many members were surveyed? MATH 1313 Finite Mathematics with Applications Find the probability that a randomly selected member: B. Always works out alone or always works out with a personal trainer. C. Works out only with a personal trainer. D. Always works out alone. 29. Three hundred college students were surveyed about the personal electronics that they used, a tablet, a smartphone and/or a portable media player. Here are the results: 294 use a smartphone 251 use a portable media player 62 use a tablet 51 use both a tablet and a portable media player 245 use both a smartphone and a portable media player 62 use both a tablet and a smartphone 51 use all three devices No students reported using none of the devices. Find the probability that a randomly selected surveyed student uses: A. Exactly 1 type of electronics. B. Exactly 2 types of electronics. C. At least 1 type of electronics. D. At least 2 types of electronics. E. At most 1 type of electronics. F. At most 2 types of electronics. G. A smartphone or a portable media player but not both, and does not use a tablet. H. A smartphone and a tablet, but not a portable media player. I. A tablet but neither of the other electronic devices. Continued on the next page... 363 Exercise Set 6.3: Rules of Probability 30. A computer store compiled data about the accessories that 500 purchasers of new tablets bought at the same time they bought the tablet. Here are the results: 411 bought cases 82 bought an extended warranty 100 bought a dock 57 bought both a dock and a warranty 65 both a case and a warranty 77 bought a case and a dock 48 bought all three accessories 58 bought none of the accessories Find the probability that a randomly selected customer bought: A. Exactly one of the accessories. B. Exactly two of the accessories. C. At least one of the accessories. D. At least two of the accessories. E. At most one of the accessories. F. At most two of the accessories. G. A case or a warranty, but not both, and did not buy a dock. H. A case but neither of the other two accessories. I. A warranty and a dock but not a case. 364 University of Houston Department of Mathematics Math 1313 Homework 19 Section 6.3 1. The choices for problem number 12 part c from the book are given below. a. 0.310 b. 0.560 c. 0.480 d. 0.720 e. 0.650 2. The choices for problem number 14 part e from the book are given below. a. 0.570 b. 0.400 c. 0.820 d. 0.980 e. 0.750 3. The choices for problem number 16 part c from the book are given below. a. 0.850 b. 0.330 c. 0.640 d. 0.780 e. 0.140 4. The choices for problem number 18 part e from the book are given below. a. 0.800 b. 0.940 c. 0.794 d. 0.410 e. 0.560 5. The choices for problem number 24 part b from the book are given below. a. 0.007 b. 0.340 c. 0.860 d. 0.904 e. 0.001 Use the following problems to answer questions 6 - 8. A group of 350 people includes 167 play the flute, 182 play the clarinet, and 86 both the flute and the clarinet. A person is selected at random. 6. What is the probability that he/she plays the flute but not the clarinet? a. 0.4213 b. 0.2314 c. 0.7812 d. 0.4587 e. 0.2743 Math 1313 Homework 19 Section 6.3 7. What is the probability that he/she plays exactly one of these types of instruments? a. 0.7821 b. 0.2457 c. 0.5057 d. 0.7879 e. 0.3645 8. What is the probability that he/she plays at least one of these instruments? a. 0.7514 b. 0.9245 c. 0.5151 d. 0.2486 e. 0.6378 Use the following problems to answer questions 9 and 10. Let E and F be two events of an experiment with sample space S. Suppose: 0.66, 0.54\tand 0.28 9. Find a. b. c. d. e. . 0.9200 1.0000 0.6600 0.6200 0.5400 10. Find a. b. c. d. e. 0.3400 0.7200 0.0800 0.2800 0.4600