lOMoARcPSD|29213696 Practice Problems IN Probability BS Civil Engineering (Mindanao State University - Iligan Institute of Technology) Studocu is not sponsored or endorsed by any college or university Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 1. A man has 3 jackets, 10 shirts, and 5 pairs of slacks. If an outfit consists of a jacket, a shirt, and a pair of slacks, how many different outfits can the man make? D. 150 A. 18 B. 30 C. 100 Probability 17. Industrial engineers are timing to workers to rank their speed at assembling computers. There are 10 workers. How many different permutations are possible? D. 3628800 A. 864000 B. 86400 C. 362880 _____ 18. The Engineering club at Midwestern University is to select a president, a vice president, and a secretary/treasurer from 38 members of the club. How many ways to select them. B. 50,616 C. 8,436 D. 1771,560 A. 73,815 _____ 19. You know that the extension of a private telephone number is 272 but you have forgotten the last 4 digits. You can only recall that the last 4 digits are 3, 6, 8, and 9 but you do not know the order. What is the maximum number of telephone calls you will need to make in order to dial the correct number? A. 20 B. 24 C. 28 D. 32 _____ 20. How many ways can 6 persons line-up If one person insists to stand in front? C. 120 D. 140 A. 80 B. 100 _____ 21. In how many different ways can one make a first, second, third, and fourth choice among 10 firms leasing construction equipment? A. 3024 B. 5040 C. 3360 D. 4210 _____ 22. The Beau Chene Garden Club has 12 members. They plan to elect a president, a vice-president, and a treasurer. How many different outcomes are possible for the election if each member is eligible for each office and no one can hold two offices? B. 1320 C. 2130 D. 2310 A. 1230 _____ 23. In how many ways can a PICE chapter with 12 directors choose a president, a vice-president, a secretary, a treasurer, and an auditor, if no member can hold more than one position? B. 95040 C. 665280 D. 845 A. 792 _____ 24. Determine the number of different words of 5 letters each that can be formed with the letters of the word chromate if each letter is used not more than once. D. 6720 A. 2670 B. 2760 C. 6270 _____ 25. How many numbers may be formed by using 4 out of the 5 digits 1, 2, 3, 4, 5 if the digits must not be repeated in any order? A. 120 B. 130 C. 140 D. 150 _____ 26. How many 4-digit numbers may be formed with the 10 digits, 0, 1, 2, 3, …, 9 if each digit is used only once in each number? C. 4536 D. 5634 A. 3456 B. 4563 _____ 27. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible? D. 2880 A. 120 B. 210 C. 280 _____ 28. In how many ways can 9 different books be arranged on a shelf so that 3 of the books are always together, A. 4230 B. 4320 C. 30240 D. 30420 _____ 29. Six different biology books, 5 different chemistry books and 2 different physics books are to be arranged on a shelf so that the biology books stand together, the chemistry books stand together, and the physics books stand together. How many such arrangements are possible? A. 1036800 B. 1306800 C. 1360800 D. 1368000 _____ 30. In how many ways can 3 boys and 2 girls sit in a row? A. 48 B. 84 C. 100 D. 120 _____ 31. Six boys and four girls are to be seated on a bench. How many ways can they be seated if the girls must be seated next to each other? A. 120960 B. 34560 C. 86400 D. 94350 _____ 32. The number of ways can 3 nurses and 4 engineers be seated on a bench with the nurses seated together is? C. 720 D. 450 A. 144 B. 258 _____ 33. Five men and 3 women are to be seated on a bench. How many ways can they be seated if the men must be seated side-by-side, and also the women? B. 1440 C. 2016 D. 4032 A. 720 _____ 2. A student has a choice of 5 foreign languages and 4 sciences. In how many ways can he choose 1 language and 1 science? A. 9 B. 10 C. 18 D. 20 _____ 3. There are 4 candidates for president of a club, 6 for vice-president and 2 for secretary. In how many ways can these three positions be filled? A. 12 B. 18 C. 24 D. 48 _____ 4. Peter is going to set up a stereo system by purchasing separate components. There are 5 different receivers, 8 different DVD players, and 12 different speaker systems. If Peter wants one of each of these components, how many different stereo systems are possible? B. 480 C. 540 D. 620 A. 360 _____ 5. Next semester you are planning to take three courses—math, English, and humanities. Based on time blocks and highly recommended professors, there are 8 sections of math, 5 of English, and 4 of humanities that you find suitable. Assuming no scheduling conflicts, how many different three-course schedules are possible? A. 17 B. 140 C. 160 D. 180 _____ 6. A music school produced a number of musicians which includes 3 drummers, 4 trumpet players and 5 pianists. How many different jazz trios can be formed from this batch of musicians if each trio consists of a drummer, a trumpet player and a pianist? A. 50 B. 60 C. 70 D. 80 _____ 7. There are three flights from Houston to Chicago, four flights from Chicago to Memphis and five flights from Memphis to Atlanta. How many choices of flights include the Houston-Chicago-MemphisAtlanta connection? C. 60 D. 150 A. 12 B. 120 _____ 8. To make a ham and cheese sandwich you are given a choice of 3 kinds of ham, 5 kinds of cheese, and 2 kinds of bread. How many different sandwiches can you make? A. 30 B. 10 C. 15 D. 45 _____ 9. How many seven-digit local telephone numbers can be formed if the first three digits are 279? A. 3024 B. 6561 C. 5040 D. 10000 _____ 10. In a certain city in the Philippines, all seven-digit telephone numbers begin with 350. How many telephone numbers maybe assigned to that city if the last four digits should not begin or end in zero? B. 8100 C. 8800 D. 9200 A. 7980 _____ 11. The LTO issues license plates consisting of letters and numbers. There are 26 letters may be repeated. There are 10 digits and the digits may be repeated. How many possible license plates can be issued with two letters followed by three numbers? A. 746,000 B. 864,000 C. 676,000 D. 542,000 _____ 12. In how many ways can 2 different prizes be awarded among 10 contestants if both may not be give to the same person? A. 19 B. 45 C. 90 D. 100 _____ 13. In how many different orders may 5 persons be seated in a row? C. 120 D. 3125 A. 24 B. 25 _____ 14. In how many ways can 7 books be arranged on a shelf? A. 4005 B. 5050 C. 5040 D. 5400 _____ 15. Twelve different pictures are available, of which 4 are to be hung in a row. In how many ways can this be done? A. 11 880 B. 12 800 C. 13 660 D. 14 600 _____ 16. An electronic controlling device requires six identical memory chips. In how many ways can this mechanism be assembled using six given chips? A. 720 B. 540 C. 360 D. 840 _____ 1 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 34. In how many ways can 5 persons be seated at a round table? A. 24 B. 48 C. 72 D. 120 _____ 35. In how many ways can 8 persons be seated at a round table if 2 particular persons must always sit together? C. 1440 D. 1360 A. 720 B. 680 _____ 36. In how many ways can 4 men and 4 women be seated at a round table if each woman is to be between two men? D. 576 A. 12 B. 144 C. 288 _____ 37. A group of engineers are taking their dinner in a big circular table. The group is composed of 4 Civil Engineers, 3 Mechanical Engineers, 2 Electrical Engineers, and 2 Electronics and Communications Engineers. How many arrangements can they form if the awesome CE’s want to be together side by side? A. 17280 B. 2880 C. 30240 D. 20160 _____ 38. There are 3 copies each of 4 different books. In how many different ways can they be arranged on a shelf? A. 366 900 B. 369 600 C. 396 600 D. 390 660 _____ 39. The Court of Appeals has 9 justices. On a certain case, the justices voted 5 to 4 in favor of the defendant. In how many ways could this have happened? B. 126 C. 134 D. 140 A. 120 _____ 40. How many permutations can be made from the letters of the word ENGINEERING? A. 39,916,800 B. 277,200 C. 55,440 D. 3,326,400 ____ Probability 51. In how many ways can a student select a set of 4 Structural Design books and 3 Hydraulics books from a set of 9 Structural Design books and 5 Hydraulics books? B. 1260 C. 1420 D. 1580 A. 1080 _____ 52. A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose from 9 men and 6 women who qualified for the position? D. 540 A. 680 B. 840 C. 480 _____ 53. In a random draw of five cards from a deck of 52 playing cards, how many ways can five red cards be drawn? A. 32890 B. 2598960 C. 1287 D. 65780 _____ 54. In a random draw of five cards from a deck of 52 playing cards, how many cards can be drawn consisting three aces and 2 face cards? B. 264 C. 426 D. 462 A. 246 _____ 55. In how many ways can a person choose 1 or more of 4 electrical appliances? A. 15 B. 16 C. 17 D. 18 _____ 56. How many ways can you invite any one or more of your eight friends to come in your birthday party? A. 255 B. 243 C. 128 D. 356 _____ 57. An amusement park has 20 different rides. How many different combinations of rides you can go on if you want to ride at least 15 of them? A. 21,700 B. 6196 C. 15,504 D. 32,767 _____ 58. In how many ways can a teacher choose one or more students from six eligible students? A. 36 B. 46 C. 63 D. 64 _____ 59. How many signals can be made with 5 different flags by raising them any number at a time? A. 235 B. 253 C. 325 D. 352 _____ 60. Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags? A. 64 B. 66 C. 68 D. 62 _____ 61. Without repeating any digit, how many 3-digit numbers can you make out from digits 0, 1, 3, 4, 8, 9 that are greater than 480 A. 47 B. 50 C. 80 D. 120 _____ 62. Without repeating any digit, how many 3-digit numbers can you make out from digits 0, 2, 3, 5, 7, 9 that are less than 730. C. 68 D. 72 A. 60 B. 64 _____ 63. How many ways can 6 persons line-up if two of those persons refuse to stand next to each other? A. 480 B. 520 C. 360 D. 440 _____ 64. In how many ways can 5 people line up to pay their electric bills, if two particular persons refuse to follow each other? B. 72 C. 90 D. 140 A. 120 _____ 65. A delegation of 4 students is selected each year from a college to attend the National Student Association annual meeting. In how many ways can the delegation be chosen if there are 12 eligible students ways but two will not attend the meeting together? A. 210 B. 240 C. 450 D. 540 _____ 66. From a group of 20 volunteers, you are choosing at least 18 to be peer counselors. In how many ways can this be done? A. 120 B. 190 C. 210 D. 211 _____ 67. In how many ways can a hostess select six luncheon guests from 10 women if she is to avoid having two of them together at the luncheon? A. 210 B. 84 C. 140 D. 168 _____ 68. In how many ways can we seat 7 people in a round table with a certain 3 people not in consecutive order? A. 576 B. 3960 C. 5320 D. 689 _____ 41. How many distinct permutations can be formed from all the letters of the word sociological? A. 9972900 B. 9997200 C. 99297200 D. 9979200 _____ 42. How many different signals, each consisting of 6 flags hung in a vertical line, can be formed from 4 identical red flags and 2 identical blue flags? A. 14 B. 28 C. 48 D. 72 _____ 43. How many different sets of 4 students can be chosen out of 17 qualified students to represent a school in a mathematics contest? A. 2380 B. 2830 C. 3280 D. 3820 _____ 44. In how many ways can 5 styles be selected out of 8 styles? A. 52 ways B. 54 ways C. 56 ways D. 58 ways _____ 45. Ayala Corporation advertised to hire financial analyst. The company received applications from 10 candidates who seem to be equally qualified. The company manager has decided to call only 3 candidates for an interview. If she randomly selects 3 candidates from the 10, how many total selections are possible? B. 120 C. 130 D. 140 A. 110 _____ 46. Determine the number of different triangles which can be formed by joining the six vertices of a hexagon, the vertices of each triangle being on the hexagon. C. 20 D. 25 A. 10 B. 15 _____ 47. In how many ways can 3 women be selected out of 15 women if 1 of the women is to be included in every selection, A. 81 B. 91 C. 101 D. 111 _____ 48. From 6 chemists and 5 biologists, a committee of 7 is to be chosen so as to include 4 chemists. In how many ways can this be done? A. 120 B. 135 C. 150 D. 175 _____ 49. Given 8 consonants and 4 vowels, how many 5-Ietter words can be formed, each word consisting of 3 different consonants and 2 different vowels? A. 20 430 B. 30 240 C. 40 320 D. 43 200 _____ 50. In a random draw of four cards from a deck of 52 playing cards, how many ways can the cards be drawn with exactly three club cards? A. 286 B. 220 C. 8800 D. 11154 _____ 2 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 Probability A. 1/6 B. 1/3 C. 2/3 D. 5/6 _____ 82. A card is drawn at random from an ordinary deck of 52 playing cards. Find the probability that it is an ace, A. 1/52 B. 1/26 C. 1/13 D. 1/12 _____ 83. A card is drawn at random from an ordinary deck of 52 playing cards. Find the probability that it is a three of clubs or a six of diamonds. A. 1/52 B. 1/26 C. 1/13 D. 1/12 _____ 84. A ball is drawn at random from a box containing 6 red balls, 4 white balls, and 5 blue balls. Determine the probability that it not red. A. 1/5 B. 2/5 C. 3/5 D. 4/5 _____ 85. Determine the probability of throwing a total of 8 in a single throw with two dice, each of whose faces is number from 1 to 6. C. 5/36 D. 7/36 A. 1/18 B. 1/9 _____ 86. Roll a pair of dice. What is the probability that the sum of two numbers is 11? A. 1/36 B. 1/9 C. 1/18 D. 1/20 _____ 87. In a throw of two dice, the probability of obtaining a total of 10 or 12 A. 1/6 B. 1/9 C. 1/12 D. 1/18 _____ 88. Eleven books, consisting of 5 engineering books, 4 mathematics books, and 2 chemistry books, are placed on a shelf at random. What is the probability that the books of each kind are all together? A. 1/1155 B. 2/1155 C. 3/1155 D. 4/1155 _____ 89. Five red blocks and 4 white blocks are placed at random in a row. What is the probability that the extreme blocks are both red? C. 5/18 D. 7/18 A. 2/9 B. 1/6 _____ 90. Nine tickets, numbered from 1 to 9, are in a box. If 2 tickets are drawn at random, determine the probability that both are odd. C. 5/18 D. 2/9 A. 3/18 B. 5/9 _____ 91. From the previous number. Find the probability that one is odd, and one is even. A. 3/18 B. 5/9 C. 5/18 D. 2/9 _____ 92. A bag contains 6 red, 4 white, and 8 blue balls. If 3 balls are drawn at random, determine the probability that all 3 are red. A. 7/204 B. 1/204 C. 5/204 D. 3/204 _____ 93. A bag contains 6 red, 4 white, and 8 blue balls. If 3 balls are drawn at random, determine the probability that 2 are white and 1 is red. A. 1/68 B. 3/68 C. 5/68 D. 7/68 _____ 94. Three cards are drawn from a pack of 52 cards. Determine the probability that all are aces. A. 1/5555 B. 1/5552 C. 1/5525 D. 1/5255 _____ 95. Three cards are drawn from a pack of 52 cards. Determine the probability that all are spades. A. 3/850 B. 7/850 C. 9/850 D. 11/850 _____ 96. Five cards are to be drawn from a deck of 52 playing cards. Find the probability that all are red cards, A. 0.01926 B. 0.02843 C. 0.06732 D. 0.02531 _____ 97. Four cards are to be drawn from a deck of 52 playing cards. Find the probability that there are exactly two clubs. A. 0.12349 B. 0.21349 C. 0.23149 D. 0.21934 _____ 98. A batch of electronic parts contains 16, which are within a power tolerance and 4, which are not. If 3 electronic parts are selected at random from the batch, compute the probability that all three are within the power tolerance. C. 28/57 D. 32/57 A. 21 B. 25/57 _____ 99. Three cards are drawn from a pack of 52, each card being replaced before the next one is drawn. Compute the probability that all are aces. D. 1/2197 A. 1/1297 B. 1/1279 C. 1/2179 _____ 100. Find the probability of drawing a 7, then a face card (K, Q or J) from a standard 52-card deck with replacement. 69. Referring to the experiment of tossing a coin twice, let A be the event “at least one head occurs”. Which of the following gives the sample space for the event A? A. {HT} B. {TH} C. {TH, HT} D. {HT, TH, HH} _____ 70. An experiment consists of selecting three items from a box of several items. The three items are classified defective (D) or non-defective (N) as they are selected. Give the sample space for the event where it has exactly one defective? A. (NNN, NND, DNN) C. (DDD, DNN, NDD) B. (DNN, NDN, NND) D. (NDD, DND, DDN) _____ 71. An experiment consists of selecting three items from a box of several items. The three items are classified defective (D) or non-defective (N) as they are selected. Give the sample space for event where it has at least two defectives in three? A. {NDD, DND, DDN} C. {NDD, DND, DDN, DDD} B. {DDN, DDD, NDD} D. {DDD} _____ 72. An experiment consists of selecting three items from a box of several items. The three items are classified defective (D) or non-defective (N) as they are selected. Give the sample space for the event where it has at most one defective? A. {NNN, NND, DNN} C. {DNN, NDN, NND, DDN, DND} B. {DNN, NDN, NND} D. {NNN, DNN, NDN, NND} _____ 73. An experiment consists of inspecting items from a production line until a defective (D) is found. Give the sample space for this experiment. What is the sample space of which exactly one item is inspected? A. {D} B. {N} C. { } D. ∅ _____ 74. An experiment consists of inspecting items from a production line until a defective (D) is found. Give the sample space for this experiment. Which outcomes are in the event of which at least two items are inspected? A. {ND, NND, NNND, NNNND} B. {ND, DN} C. {ND, NND, NNND, NNNND, …} D. {D, ND} _____ 75. An experiment consists of inspecting items from a production line until a defective (D) is found. Give the sample space for this experiment. Which outcomes are in the event of which at most five items are inspected? A. {D, ND, NND, NNND, NNNND} B. {DNNNN, NDNNN, NNDNN, NNNDN, NNNND} C. {NNNND, NNNDD, NNDDD, NNDDD, DDDDD} D. {NNNND} _____ 76. Suppose a lot consisting of 100 items contains 5 defectives. If one item is randomly selected, the probability P(item is defective) is: A. 0.05 B. 0.5 C. 0.005 D. 0.0005 _____ 77. If a die is rolled 5 times, what is the probability of obtaining five 6s in a row? Ans. (1/6)⁵ _____ 78. A dart target board consists of a center circle having a radius of 2 inches a square section with dimension of 6 in x 6 in and the radius of the biggest circle is 6 in. The three cross-sections have the same center at 0. Assuming the dart is equally likely to hit any point inside the target. Find the probability that a dart thrown at the circular target will hit the area outside the square. Ans. 0.682 _____ 79. An employee of a large company, Toyota Motors Inc., is promoted to management and will be transferred within 6 months. The employee is told that there is a 33% probability of being transferred to Cebu and a 50% probability of being transferred to Davao. What is the probability that the employee will be transferred to Cebu or Davao? Ans. 0.83 _____ 80. In an unbiased coin toss, the probability of getting heads or tails is exactly ½. A coin is tossed and one gets heads. If the coin is tossed again, the probability of getting head again is: A. ½ B. 0 C. ¼ D. ⅓ _____ 81. A single die is tossed once. Find the probability of a 2 or 5 turning up. 3 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 A. 0.0167 B. 0.0178 C. 0.0181 D. 0.0195 _____ 101. The probability that a certain man will be alive 25 years hence is 3/7, and the probability that his wife will be alive 25 years hence is 4/5. Determine the probability that, 25 years hence, at least one of them will be alive. A. 3/35 B. 4/35 C. 31/35 D. 32/35 _____ 102. A component fails a particular test (A) 15% of the time or a component displays strain but does not fail the test (B) 25% of the time. (a) What is the probability that the component does not fail the test? (b) What is the probability that a component works perfectly (neither displays strain nor fails the test)? (c) What is the probability that the component either fails or shows strain in the test? Answers: (a) 0.85 (b) 0.6 (c) 0.4 _____ 103. A box contains 58 red marbles, 14 yellow marbles, 28 blue marbles, all the marbles are of the same size. Three marbles are drawn at random from the box, first one, then a second, and then a third. Determine the probability of getting one red marble, one yellow marble, and one blue marble with replacement. A. 0.0145 B. 0.0227 C. 0.0348 D. 0.0425 _____ 104. A classroom contains 71 students. 10 of them are Chinese, 24 are Japanese and 37 are Filipinos. If three students are randomly asked to get out of the room, one after the other, what are the probabilities that all 3 students are Chinese? A. 0.00021 B. 0.00032 C. 0.0036 D. 0.0042 _____ 105.A box contains 100 washers, 24 of which are brass, 36 copper, and the remainder are steel. One washer is taken at random and retained, and a second washer similarly drawn. Determine the probability that the first is brass, and the second is copper. A. 0.1296 B. 0.0873 C. 0.0864 D. 0.1936 _____ 106. A box contains 74 brass washers, 86 steel washers, and 40 aluminum washers. Three washers are drawn at random from the box with replacement. Find the probability that there are no aluminum washers drawn. A. 0.4819 B. 0.5101 C. 0.5852 D. 0.6652 _____ 107. Nine pingpong balls number are placed in tambulo. You randomly draw two balls. What is the probability that the first number is odd and the second number is even if there is a replacement for the first ball before selecting the second? A. 0.247 B. 0.274 C. 0.427 D. 0.472 _____ 108. A quality engineer selects 3 iPods from a box that contains 20 iPods of which 3 are defective. What is the probability that the first is defective and the others are not defective? A. 0.295 B. 0.204 C. 0.119 D. 0.122 _____ 109. A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects two cell phones at random without replacement. What is the probability that neither is defective? C. 0.00066 D. 0.00051 A. 0.95063 B. 0.9505 _____ 110. A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects two cell phones at random without replacement. What is the probability that both are defective A. 0.00050 B. 0.0007 C. 0.00053 D. 0.00063 _____ 111. A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects two cell phones at random with replacement. What is the probability that neither is defective? A. 0.950625 B. 0.9505 C. 0.00066 D. 0.00051 _____ 112. A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects two cell phones at random with replacement. What is the probability that both are defective A. 0.00050 B. 0.0007 C. 0.00053 D. 0.000625 _____ 113. A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects two cell phones at random without replacement. What is the probability that exactly one is defective? A. 0.0245 B. 0.0490 C. 0.0488 D. 0.0244 _____ Probability 114. A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects two cell phones at random with replacement. What is the probability that exactly one is defective? C. 0.04875 D. 0.0244 A. 0.0245 B. 0.0490 _____ 115. A man holds 2 of a total of 20 tickets in a lottery. If there are 2 winning tickets, determine the probability that he has exactly one. A. 9/95 B. 12/95 C. 15/95 D. 18/95 _____ 116. There are three candidates, A, B, and C, for an office. The odds that A will win are 7 to 5, and the odds that B will win are 1 to 3. (a) What is the probability that either A or B will win? B. 5/6 C. 6/48 D. 6/7 A. 7/48 _____ 117. An urn contains 4 black balls and 6 white balls. What is the probability of getting 1 black and 1 white ball in two consecutive draws from the urn? C. 0.53 D. 0.04 A. 0.24 B. 0.27 _____ 118. One bag contains 4 white balls and 2 black balls; another bag contains 3 white balls and 5 black balls. If one ball is drawn from each bag, determine the probability that 1 is white and 1 is black. C. 13/24 D. 17/24 A. 7/24 B. 11/24 _____ 119. From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that one ball is white and one ball is black. Assume that the first ball is returned before the second ball is drawn. A. 16/81 B. 25/81 C. 20/81 D. 40/81 _____ 120. One bag contains 5 white balls and 4 black balls and a second bag contains 2 white and 4 black balls. One ball is drawn from the second bag and is placed unseen in the first bag. What is the probability that the ball now drawn from the first bag is white? A. 5/21 B. 8/15 C. 23/63 D. 1/15 _____ 121. One purse contains 5 dimes and 2 quarters, and a second purse contains 1 dime and 3 quarters. If a coin is taken from one of the two purses at random, what is the probability that it is a quarter? A. 29/56 B. 29/65 C. 32/65 D. 23/56 _____ 122. One purse contains 6 copper coins and 1 silver coin; a second purse contains 4 copper coins. Five coins are drawn from the first purse and put into the second, and then 2 coins are drawn from the second and put into the first. Determine the probability that the silver coin is in the second purse. A. 1/9 B. 2/9 C. 4/9 D. 5/9 _____ 123. From the previous problem. Determine the probability that the silver coin is in the second purse. C. 4/9 D. 5/9 A. 1/9 B. 2/9 _____ 124. A box contains 7 tickets, numbered from 1 to 7 inclusive. If 3 tickets are drawn from the box, one at a time, determine the probability that they are alternately either odd, even, odd or even, odd, even. A. 1/7 B. 2/7 C. 3/7 D. 4/7 _____ 125. The probability that A can be solve a given problem is 4/5, that B can solve it is 2/3, and that C can solve it is 3/7. If all three try, computer the probability that the problem will be solved. C. 101/105 D. 104/105 A. 92/105 B. 97/105 _____ 126. What is the probability of getting at least 1 one in 2 throws of a die? A. 11/36 B. 13/36 C. 23/36 D. 26/36 _____ 127. The probability of A's winning a game of chess against B is 1/3. What is the probability that A will win at least 1 of a total of 3 games? A. 8/27 B. 11/27 C. 16/27 D. 19/27 _____ 128. Find the probability that in tossing a fair coin three times, there will appear at least 1 head. A. 7/8 B. 2/3 C. 5/8 D. 1/3 _____ 129. Find the probability that in a family of 4 children there will be at least 1 boy. Assume that the probability of a male birth is ½.. D. 15/16 A. 9/16 B. 11/16 C. 13/16 _____ 130. Find the probability of getting a total of 7 at least once in three tosses of a pair of fair dice. 4 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 Probability whole lot are perfect, what is the probability that the lot will be accepted? A. 0.581 B. 0.851 C. 0.729 D. 0.927 A. 91/126 B. 91/216 C. 95/126 D. 95/216 _____ 131. If the probability that the average freshman will not complete four years of college is 1/3, what is the probability p that of 4 freshmen at least 3 will complete four years of college? C. 16/27 D. 19/27 A. 8/27 B. 11/27 _____ 132. The probability of getting exactly 2 heads in 6 tosses of a fair coin is A. 11/64 B. 13/64 C. 15/64 D. 17/64 _____ 133. Find the probability that in five tosses of a fair die, a 3 will appear twice. A. 625/3888 B. 265/3888 C. 345/3888 D. 435/3888 _____ 134. Find the probability that in five tosses of a fair die, a 5 will appear at most once, A. 1235/3888 B. 1325/3888 C. 2135/3888 D. 3125/3888 _____ 135. According to statistics 30% of smokers want to quit smoking. In a random of 12 smokers, what is the probability that the number of who want to quit smoking is exactly 6? A. 0.0792 B. 0.0836 C. 0.0942 D. 0.0632 _____ 136. Sixty percent of the employees of a certain company have at least one credit card. If a random sample of 12 employees, what is the probability that 5 of them have at least one credit card? D. 0.1009 A. 0.9100 B. 0.1900 C. 0.1090 _____ 137. If the probability that it will rain on any given day this week is 60%, find the probability that it will rain exactly 3 out of 7 days this week. A. 0.1359 B. 0.1593 C. 0.1935 D. 0.1953 _____ 138. An automatic machine produces an average 10% of its components outside of tolerance required. In a sample of 10 components from the machine, determine the probability of having 3 components outside of tolerance required. B. 0.0574 C. 0.0745 D. 0.0754 A. 0.0475 _____ 139. Calculate the probability of randomly guessing at least 7 correct answers on a 10-question true or false quiz to get a passing a grade. A. 0.127 B. 0.172 C. 0.712 D. 0.721 _____ 140. A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the city. What is the probability that fewer than 4 of the next 9 vehicles are from out of the city? D. 0.8343 A. 0.3483 B. 0.3834 C. 0.4833 _____ 141. If 20% of the bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random, less than 2, bolts will be defective. C. 0.8192 D. 0.9821 A. 0.1892 B. 0.2981 _____ 142. Teams A and B are playing in a league. They will pay each other 5 times. If the probability that A wins a game is ⅓, what is the probability that team A will win at least three of the five games? A. 0.12 B. 0.21 C. 0.34 D. 0.43 _____ 143. It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have at least 6 contaminated chickens? A. 0.1178 B. 0.1718 C. 0.1781 D. 0.1871 _____ 144. A manufacturer has the following quality control check at the end of a production line: If at least eight of ten randomly picked articles meet all specifications, the whole shipment is approved. If, in reality, 85% of a particular shipment meet all specifications, what is the probability that the shipment will make it through the control check? A. 0.280 B. 0.370 C. 0.820 D. 0.730 _____ 145. A grocery store manager notes that 35% of customers who buy a particular product make use of a store coupon to receive a discount. If seven people purchase the product, what is the probability that fewer than four will use a coupon? A. 0.60 B. 0.70 C. 0.80 D. 0.90 _____ 146. An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition. If in reality 90% of the _____ 147. A box contains 5 red balls, 4 white balls, and 3 blue balls. A ball is selected at random from the box, its color is noted, and then the ball is replaced. Find the probability that out of 6 balls selected in this manner, 3 are red, 2 are white, and 1 is blue. A. 325/5184 B. 425/5184 C. 725/5184 D. 625/5184 _____ 148. A fair is thrown 5 times. On any one throw, outcome 1 is that an even number appears, outcome 2 is that a 1 or 3 appears, and outcome 3 is that a 5 appears. Find the probability that in the 5 throws, outcome 1 occurs twice, outcome 2 occurs twice, and outcome 3 occurs once. A. 0.888143 B. 0.148838 C. 0.138848 D. 0.1888889 _____ 149. If a fair die is to be tossed 12 times, the probability of getting 1, 2, 3, 4, 5 and 6 points exactly twice each is A. 0.00344 B. 0.00434 C. 0.00334 D. 0.00343 _____ 150. Based on past experience, the makeup of Dr. Stephens’ statistics for engineers class has consisted of 20% civil engineers, 30% chemical engineers, 40% industrial engineers, and 10% electrical engineers. Given that these probabilities still hold, what is the probability that her 2010 classes will consist of 25 civil engineers, 30 chemical engineers, 40 industrial engineers, and 10 electrical engineers? A. 0. 00047 B. 0.00074 C. 0.00036 D. 0.00063 _____ 151. The probabilities that the light bulb of the projector used in Dr. Stephen’s statistical engineering software course will last less than 40 hours, 40 to 80 hours, or more than 80 hours are 0.3, 0.5, and 0.2. Find the probability that among 8 such bulbs, 2 will last less than 40 hours, 5 will last between 40 and 80 hours, and 1 will last more than 80 hours. A. 0.0459 B. 0.0594 C. 0.0549 D. 0.0945 _____ 152. A traffic engineer knows that at a certain intersection over a 24-hour period, no accidents occur within probability 0.25, one accident occurs with probability 0.60, and two or more accidents occur with probability of 0.15. What is the probability that over ten 24-hour periods, no accidents occur 3 times, one accident occurs 6 times and two or more accidents occur once? A. 0.01968 B. 0.25000 C. 0.01094 D. 0.09185 _____ 153. A traffic engineer is studying accidents and finds that 15% are 1-car accidents, 65% are 2-car accidents, 15% are 3-car accidents, and 5% are 4-car accidents in the area he is studying. He randomly selects 10 accidents. Find the probability that in the 10 selected, 2 are 1-car accidents, 5 are 2-car accidents, 2 are 3 car accidents, and 1 is 4-car accidents. B. 0.0222 C. 0.0333 D. 0.0444 A. 0.0111 _____ 154. Items under inspection are subjected to two types of defects. About 70% of the items in a large lot are defect-free, 20% have a type A defect, and 10% have a type B defect. Six of the items are randomly selected. Find the probability that 3 have no defects, 1 has a type A defect, and 2 have a type B defect. A. 0.014 B. 0.023 C. 0.032 D. 0.041 _____ 155. Suppose only 12% of men in ancient Greece were honest. What is the probability that the first honest man he encounters will be no later than the fourth man he meets? B. 0.4003 C. 0.5006 D. 0.6005 A. 0.3004 _____ 156. A box contains 6 blue marbles and 4 red marbles. An experiment is performed in which a marble is chosen at random and its color observed, but the marble is not replaced. Find the probability that after 5 trials of the experiment, 3 blue marbles will have been chosen. A. 5/21 B. 8/21 C. 10/21 D. 13/21 _____ 157. A janitor with a bunch of 9 keys is to open a door but only one key can open. What is the probability that he will succeed in 3 trials? A. 0.375 B. 0.425 C. 0.333 D. 0.111 _____ 158. Ten percent of the tools produced in a certain manufacturing process turn out to be defective. Find the probability that in a sample of 10 tools chosen at random, exactly 2 will be defective, by using the Poisson distribution. A. 0.1398 B. 0.1839 C. 0.3198 D. 0.3918 5 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 Probability 173. A trucking firm determines that its fleet of trucks averages a mean of 12.4 miles per gallon with a standard deviation of 1.2 miles per gallon on cross-country hauls. What is the probability that one of the trucks averages fewer than 10 miles per gallon? A. 0.0228 B. 0.0339 C. 0.0446 D. 0.0552 _____ 174. A factory dumps an average of 2.43 tons of pollutants into a river every week. If the standard deviation is 0.88 tons, what is the probability that in a week more than 3 tons are dumped? A. 0.2578 B. 0.2875 C. 0.5287 D. 0.5827 _____ 175. An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hour, what is the probability that an item will take between 3 and 4 hours? A. 0.37607 B. 0.67307 C. 0.70367 D. 0.77603 _____ 176. The mean weight of 500 male students at a certain college is 151 lb and the standard deviation is 15 lb. Assuming that the weights are normally distributed, find how many students weigh between 120 and 155 lb B. 300 C. 320 D. 340 A. 280 _____ 177. The mean inside diameter of a sample of 200 washers produced by a machine is 0.502 inches and the standard deviation is 0.005 inches. The purpose for which these washers are intended allows a maximum tolerance in the diameter of 0.496 to 0.508 inches, otherwise the washers are considered defective. Determine the percentage of defective washers produced by the machine, assuming the diameters are normally distributed. B. 23% C. 25% D. 28% A. 21% _____ 178. A large batch of electric light bulbs has a mean time of failure of 2400 hours and a standard deviation of 320 hours. If a random sample of 40 light bulbs is drawn from the batch, determine the probability that the mean time of failure will be less than 2300 hours. A. 0.032 B. 0.015 C. 0.024 D. 0.047 _____ 179. A large batch of electric light bulbs has a mean time of failure of 2400 hours and the standard deviation of 60 hours for a batch of 4200 bulbs. How many light bulbs will likely last more than 2500 hours? A. 201 B. 256 C. 183 D. 154 _____ 180. In normal random distribution, it is found out that the mean is 80 and standard deviation is 5, which of the following ranges in which 84% of the data lies? B. 65 - 85 C. 70 - 90 D. 75 – 95 A. 60 - 80 _____ 181. What is the standard deviation of the normal distribution that approximates a binomial distribution consisting of 119 trials within probability of 0.70 of success? C. 5 D. 6 A. 3 B. 4 _____ 182. Compute the standard deviation of the normal distribution that approximates a binomial distribution. There are 60 trials with a probability of failure of 0.25. A. 2.45 B. 3.35 C. 4.25 D. 5.15 _____ 183. Of the coral reef species on the Great Barrier Reef off Australia, 73% are poisonous. If at mist boat taking divers to different points off the reef encounters an average of 25 coral reef species, what are the mean and standard deviation for he expected number of poisonous species seen? A. μx = 6.75, σx = 4.93 C. μx = 18.25, σx = 4.93 B. μx = 18.25, σx = 2.22 D. μx = 18.25, σx = 8.88 _____ 184. A die is tossed 120 times. Find the probability that the face 4 will turn up 18 times or less, assuming the die is fair. A. 0.3557 B. 0.5337 C. 0.5773 D. 0.7553 _____ 185. A fair coin is tossed 500 times. Find the probability that the number of heads will not differ from 250 by more than 10. A. 0.2586 B. 0.5268 C. 0.6528 D. 0.8265 _____ 186. If 60% of the population support massive federal budget cuts, what is the probability that in a survey of 250 people at most 155 people support such cuts? B. 0.7611 C. 0.7822 D. 0.8722 A. 0.6711 _____ _____ 159. If the probability that an individual will suffer a bad reaction from injection of a given serum is 0.001, determine the probability that out of 2000 individuals exactly 3 individuals will suffer a bad reaction. C. 0.180 D. 0.190 A. 0.160 B. 0.170 _____ 160. From the previous problem, determine the probability that out of 2000 individuals more than 2 individuals will suffer a bad reaction. A. 0.232 B. 0.323 C. 0.454 D. 0.545 _____ 161. A manufacturer estimates that 0.25% of his output of a component are defective. The components are marketed in packets of 200. Using Poisson’s distribution, determine the probability of a packet containing only 2 defective components. B. 0.758 C. 0.0785 D. 0.0857 A. 0.578 _____ 162. If 3% of the electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs, 4 bulbs will be defective. A. 0.168 B. 0.178 C. 0.718 D. 0.816 _____ 163. From the previous problem, find the probability that in a sample of 100 bulbs, more than 5 bulbs will be defective. A. 0.0398 B. 0.0839 C. 0.0893 D. 0.0983 _____ 164. A manufacturer estimates that 1.5% of his output of a small item is defective. Find the probabilities that in a pack of 200 items, three or more are defective. D. 0.577 A. 0.224 B. 0.423 C. 0.1494 _____ 165. The number of cars entering the tool plaza on a bridge during the hour after midnight follows a Poisson distribution with a mean of 20. What is the probability that 17cars will pass through the toll plaza during that hour on any given night. A. 6.7% B. 7.6% C. 8.9% D. 9.8% _____ 166. The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 3. Find the probability that exactly five road construction projects are currently taking place in this city. A. 0.100532 B. 0.100819 C. 0.200521 D. 0.200829 _____ 167. The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 7. Find the probability that more than four road construction projects are currently taking place in the city. C. 0.827 D. 0.872 A. 0.728 B. 0.782 _____ 168. Suppose the number of babies born during an 8-hour shift at a hospital's maternity wing follows a Poisson distribution with a mean of 6 an hour. Find the probability that five babies are born during a particular 1-hour period in this maternity wing. D. 0.1606 A. 0.1303 B. 0.1404 C. 0.1505 _____ 169. The university policy department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.8 tickets per day. Find the probability that less than six tickets are written on a randomly selected day from this distribution. B. 0.1284 C. 0.1428 D. 0.1482 A. 0.1248 _____ 170. A lathe machine in a mechanical shop breaks down an average of 4 times per year. Using Poissons distribution, find the probability that at most 1 breakdown will occur each year. A. 0.1079 B. 0.1709 C. 0.1907 D. 0.1970 _____ 171. Communications engineers have determined that lifetimes of Ace cell phones are normally distributed with a mean equal to 60 months and a standard deviation equal to 5 months. What is the probability that a cellphone of this type has lifetime less than 55 months? A. 0.29602 B. 0.84134 C. 0.34134 D. 0.15866 _____ 172. The amount of time that a teenager plays videogames in any given week is normally distributed. If a teenager plays videogames an average of 15 hours per week with a standard deviation of 3 hours, what is the probability of a teenager playing videogames between 9 and 21 hours? B. 95.4% C. 96.5% D. 97.9% A. 94.5% _____ 6 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 187. Health official from DOH who have studied a particular virus say that 50% of all the Filipino people have had the virus. If a random of 144 people is taken, what is the probability that fewer than 60 had the virus? A. 0.023 B. 0.032 C. 0.045 D. 0.054 _____ 188. Among 10,000 random digits, find the probability that the digits 3 appear at most 950 times. A. 0.4467 B. 0.4647 C. 0.4746 D. 0.4764 _____ 189. In 2017, about 1 in 43 births resulted in twins. If a barangay has 2150 births that year, find the probability that between 29 and 50 of them were twins. B. 0.4987 C. 0.7489 D. 0.7984 A. 0.4789 _____ 190. One thousand copper rods have the properties shown in the table. Diameter Too thin OK Too thick Length Too short 10 5 5 OK 40 902 7 Too long 4 20 7 If the rod meets the length specifications, find the probability the rod meets the diameter specifications. B. 0.95 C. 0.96 D. 0.97 A. 0.94 _____ 191. From the previous problem. If the meets the diameter specifications, find the probability the rod meets the length specifications. A. 0.94 B. 0.95 C. 0.96 D. 0.97 _____ 192. On the East Coast, it is known from health records that the probability of selecting an adult over 40 years of age with cancer is 0.05. The probability of diagnosing a person with cancer as having the disease is 0.78 and the probability of incorrectly diagnosing a person without cancer as having the disease is 0.06. Find the probability that a person is diagnosed as having cancer. A. 0.0390 B. 0.0570 C. 0.0960 D. 0.0620 _____ 193. From the previous problem. Find the probability that a person diagnosed as having cancer actually has the disease? A. 0.59375 B. 0.40625 C. 0.3690 D. 0.2755 _____ 194. Suppose that, in a certain part of the world, any 50-year period the probability of a major plague is .39, the probability of a major famine is .52, and the probability of both a plague and a famine is .15. What is the probability of a famine given that there is a plague? A. .288 B. .385 C. .513 D. .760 _____ 195. A process manufactures aluminum cans. The probability that a can has a flaw on the side is 0.02, the probability that it has a flaw on the top is 0.03, and the probability that it has a flaw on the top and the side is 0.01. What is the probability that a can will have flaw on its side, given that it has a flaw on the top? A. 3/50 B. 1/25 C. 1/2 D. 1/3 _____ 196. A box contains black chips and red chips. A person draws two chips without replacement. If the probability of selecting a black chip and a red chip is 15/56 and the probability of drawing a black chip on the first draw is 3/4, what is the probability of drawing a red chip on the second draw, if you know the first chip drawn was black? A. 3/14 B. 5/14 C. 9/14 D. 11/14 _____ 197. The probability that a student takes chemistry and is on the honor rolls is 0.042. The probability that a student is on the honor roll is 0.21. What is the probability that the student is taking chemistry, given that the student is on the honor roll? B. 0.20 C. 0.30 D. 0.40 A. 0.10 _____ 198. In a certain college, 5% of the men and 2% of the women took engineering. Furthermore, 60% of the students are men. If a student is selected at random, and is found to be an engineering student, what is the probability that the student is a man? A. 15/19 B. 3/10 C. 16/19 D. 4/13 _____ 199. At the Pine Valley Country Club, 32% of the members play golf and are female. Also, 80% of the members play golf. If a member of the club is selected at random, find the probability that the member is female give that the member plays golf. D. 0.40 A. 0.10 B. 0.20 C. 0.30 _____ Probability 200. In a certain region of the country it is known from experience that the probability of selecting an adult over 40 years of age with a cancer is 0.02. If the probability of a doctor correctly diagnosing a person with a cancer as having the disease is 0.78 and the probability of incorrectly diagnosing a person without cancer as having the disease is 0.06, what is the probability that a person is diagnosed as having cancer? B. 7.44% C. 10.34% D. 22.88% A. 16.28% _____ 201. A plant has three suppliers. S1 supplies 30% of the parts of the plant, S2 supplies 50% of the parts, and S3 supplies the remaining 20%. One percent of the parts supplied by S1 are defective, two percent of the parts supplied by S2 are defective, and three parts supplied by S3 are defective. Given that the part was defective, what is the probability that it came from supplier S3? A. 0.5263 B. 0.4737 C. 0.1579 D. 0.3158 _____ 202. A Ford has engines in three sizes. Of the Ford cars sold, 50% have the smallest engine, 40% have the medium engine. Of the cars with the smallest engine, 15% fail an emissions test within two years of purchase. The failure figure for medium size engines is 10%, and the failure figure for the largest engines is 5%. What is the probability that this Ford will fail the emissions test within two years? A. 0.12 B. 0.20 C. 0.18 D. 0.22 _____ 203. If the probability of a spacecraft being struck by exactly one cosmic particle during and Earth-Neptune roundtrip is identical to its probability of not being struck at all, what is this probability? A. 0.368 B. 0.135 C. 0.513 D. 0.638 _____ 204. On a university campus, 60%, 30%, and 10% of the computers use Windows, Apple, and Linux operating systems, respectively. A new virus affects 3% of the Windows, 2% of the Apple, and 1% of the Linux operating systems. What is the probability a computer on this campus has the virus? A. 0.036 B. 0.025 C. 0.063 D. 0.052 _____ 205. A chemical supply company ships a chemical in 5-gallon drums. X represents the number of drums ordered by a randomly chosen customer. X has the following distribution. X 1 2 3 4 5 P(X) .1 .1 .2 .2 .4 Find the mathematical expectation of X. A. 3.2 B. 3.5 C. 3.7 D. 3.9 _____ 206. The group of engineers decide to play the game of craps. A pair of dice is rolled in this game and the sum to appear on the dice is of interest. What is the mathematical expectation of the sum to appear when the dice are rolled? C. 7 D. 8 A. 5 B. 6 _____ 207. How many people would you expect to meet before you met one who was born on a Wednesday? A. 6 B. 7 C. 10 D. 14 _____ 208. The number of defective welds in a length of pipe 0 through 6 with the following probabilities. X 0 1 2 3 4 5 6 P(X) 0.60 0.30 0.05 0.02 0.01 0.01 0.01 Find the expected value of the number of defective welds. D. 0.61 A. 0.52 B. 0.55 C. 0.59 _____ 209. The probability that a relay remains open is 0.5. An electrical circuit consist of three such relays. The number of relays that remain open in three are 0, 1, 2, or 3. The number of relays that remain open is represented by X. The number of relays that remain open has the following values with the probabilities. X 0 1 2 3 P(X) 0.125 0.375 0.375 0.125 Find the expected value of the number of open relays. A. 1.00 B. 1.25 C. 1.50 D. 1.75 _____ 210. A game is played as follows. You pay $1 to play. A coin is flipped four times. If four tails or four heads are obtained, you get your 1$ back plus $5 more. Otherwise you forfeit your $1. What it the mathematical expectation? A. 0.25 B. 0.75 C. -0.25 D. 0.50 7 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph) lOMoARcPSD|29213696 Gillesania Engineering Review and Training Center ‐ 2022 Probability _____ 212. Assuming that each packet of cigarettes from a certain manufacturer contains, as a premium, one of a set of 52 playing cards, and that these cars are distributed among the packets at random (the number of packets available being infinite), what is the average minimum number of packets that must be purchased in order to obtain a complete set of cards? A. 236 B. 263 C. 326 D. 36 _____ 211. An engineering company prepares an estimate for a job. The cost of preparing the estimate is P10,000. The amount of profit over and above the P10,000 is P25,000, if their estimate is accepted. The probability that their estimate will be accepted is 0.70 and the probability that their estimate will not be accepted is 0.30. What is the expected profit? A. P 14,500 B. P 15,200 C. P 15,800 D. P 16,500 8 Downloaded by Allyssa Mae Biron (allyssamaebacay.biron@bicol-u.edu.ph)