Probability.docx

PROBABILITY 1. In a class 40 students, 27 like Calculus and 25 like Chemistry. How many like both Calculus and Chemistry? A. 10 B. 11 C. 12 D. 13 2. A club of 40 executives, 33 like to smoke Marlboro and 20 like to smoke Philip Morris. How many like both? A. 10 B. 11 C. 12 D. 13 3. A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q? A. 20 B. 22 C. 24 D. 26 4. The probability for the ECE board examinees from a certain school to pass the subject Mathematics is 3/7 and for the subject Communications is 5/7. If none of the examinees fails both subject and there are 4 examinees who pass both subjects, find the number of examinees from that school who took the examinations. A. 20 B. 25 C. 30 D. 28 5. In a commercial survey involving 1000 persons on brand preference, 120 were found to prefer brand x only, 200 prefer brand y only, 150 prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x and 370 prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of the three brands? A. 280 B. 230 C. 180 D. 130

6. A toothpaste firm claims that in survey of 54 people, they were using either Colgate, Hapee or Close-up brand. The following statistics were found: 6 people used all three brands, 5 used only Hapee and Close-up, 18 used Hapee or Close-up, 2 used Hapee, 2 used only Hapee and Colgate, 1 used Close-up and Colgate, and 20 used only Colgate. Is the survey worth paying for? A. Neither yes nor no B. Yes C. No D. Either yes or no 7. How many four-letter words beginning and ending with a vowel without any letter repeated can be formed from the word “personnel”? A. 40 B. 480 C. 20 D. 312 8. Five different Mathematics books, 4 different electronics books and 2 different communications books are to be placed in a shelf with the books of the same subject together. Find the number of ways in which the books can be placed. A. 292 B. 5760 C. 34560 D. 12870 9. The number of ways can 3 nurses and 4 engineers be seated on a bench with the nurses seated together is? A. 144 B. 258 C. 720 D. 450 10. If 15 people won prizes in the state lottery (assuming that there are no ties), how many ways can these 15 people win first, second, third, fourth and fifth prizes? A. 4,845 B. 116,260 C. 360,360 D. 3,003 11. How many 4 digit numbers can be formed without repeating any digit from the following digits: 1, 2, 3, 4 and 6? A. 120 B. 130 C. 140 D. 150

12. How many permutations are there if the letters PNRCSE are taken six at a time? A. 1440 B. 480 C. 720 D. 360 13. In how many ways can 6 distinct books be arranged in a bookshelf? A. 720 B. 120 C. 360 D. 180 14. What is the number of permutations of the letters in the word BANANA? A. 36 B. 60 C. 52 D. 42 15. A PSME unit has 10 ME’s, 8 PME’s and 6 CPM’s. If a committee of 3 members, one from each group is to be formed, how many such committees can be formed? A. 2,024 B. 12,144 C. 480 D. 360 16. In how many ways can a PSME Chapter with 15 directors choose a President, a Vice President, a Secretary, a Treasurer and an Auditor, if no member can hold more than one position? A. 360,360 B. 32,760 C. 3,003 D. 3,603,600 17. 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 18. In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats? A. 1152 B. 2304 C. 576 D. 2204

19. There are four balls of four different colors. Two balls are taken at a time and arranged in a definite order. For example, if a white and red balls are taken, one definite arrangement is white first, red second, and another arrangement is red first, white second. How many such arrangements are possible? A. 24 B. 6 C. 12 D. 36 20. How many different ways can 5 boys and 5 girls form a circle with boys and girls alternate? A. 28,800 B. 2,880 C. 5,600 D. 14,400 21. There are four balls of different colors. Two balls at a time are taken and arranged any way. How many such combinations are possible? A. 36 B. 3 C. 6 D. 12 22. How many 6-number combinations can be generated from the numbers from 1 to 42 inclusive, without repetition and with no regards to the order of the numbers? A. 850,668 B. 5,245,786 C. 188,848,296 D. 31,474,716 23. Find the total number of combinations of three letters, J, R, T taken 1, 2, 3 at a time. A. 7 B. 8 C. 9 D. 10 24. In how many ways can you invite one or more of your five friends in a party? A. 15 B. 31 C. 36 D. 25

25. In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be formed from four chemical engineers and three mechanical engineers? A. 18 B. 64 C. 32 D. None of these 26. In Mathematics examination, a student may select 7 problems from a set of 10 problems. In how many ways can he make his choice? A. 120 B. 530 C. 720 D. 320 27. How many committees can be formed by choosing 4 men from an organization of a membership of 15 men? A. 1390 B. 1240 C. 1435 D. 1365 28. 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? A. 680 B. 540 C. 480 D. 840 29. There are 13 teams in a tournament. Each team is to play with each other only once. What is the minimum number of days can they all play without any team playing more than one game in any day? A. 11 B. 12 C. 13 D. 14 30. There are five main roads between the cities A and B, and four between B and C. In how many ways can a person drive from A to C and return, going through B on both trips without driving on the same road twice? A. 260 B. 240 C. 120 D. 160

31. There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns 5 tickets? A. 50% B. 25% C. 20% D. 40% 32. 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 33. Roll two dice once. What is the probability that the sum is 7? A. 1/6 B. 1/8 C. 1/4 D. 1/7 34. In a throw of two dice, the probability of obtaining a total of 10 or 12 is? A. 1/6 B. 1/9 C. 1/12 D. 1/18 35. Determine the probability of drawing either a king or a diamond in a single draw from a pack of 52 playing cards A. 2/13 B. 3/13 C. 4/13 D. 1/13 36. A card is drawn from a deck of 52 playing cards, Find the probability if drawing a king or a red card. A. 0.5835 B. 0.5385 C. 0.3585 D. 0.8535 37. A coin is tossed 3 times. What is the probability of getting 3 tails up? A. 1/8 B. 1/16 C. 1/4 D. 7/8

38. The probability of getting at least 2 heads when a coin is tossed four times is? A. 11/16 B. 13/16 C. 1/4 D. 3/8 39. A fair coin is tossed three times. What is the probability of getting either 3 heads or 3 tail? A. 1/8 B. 3/8 C. 1/4 D. 1/2 40. The probability of getting a credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of them got a credit? A. 19/27 B. 8/27 C. 2/3 D. 1/3 41. There are 3 questions in a test. For each question is awarded for a correct answer and none for a wrong answer. If the probability that Janine correctly answers a question in the test is 2/3, determine the probability that she gets zero in the test. A. 8/27 B. 4/9 C. 1/30 D. 1/27 42. In the ECE Board Examinations, the probability that an examinee will pass each subject is 0.8. What is the probability that an examinee will pass at least two subjects out of three board subjects? A. 70.9% B. 80.9% C. 85.9% D. 89.6% 43. In a multiple choice test, each question is to be answered by selecting 1 out of 5 choices of which only 1 is right, If there are 10 questions in a test, what is the probability of getting 6 right of pure guesswork? A. 10% B. 6% C. 0.44% D. 0.55%

44. From a box containing 6 red balls, 8 white balls and 10 blue balls, one ball is drawn at random. Determine the probability that is red or white. A. 1/3 B. 7/12 C. 5/12 D. 1/4 45. From a bag containing 4 black balls and 5 white balls, two balls are drawn one at a time. Find the probability that both balls are white. Assume that the first ball is returned before the second ball is drawn. A. 25/81 B. 16/81 C. 5/18 D. 40/81 46. A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black? A. 5/16 B. 5/28 C. 5/32 D. 5/14 47. 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? A. 0.24 B. 0.27 C. 0.53 D. 0.04 48. 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 49. A group of 3 people enter a theatre after the lights had dimmed. They are shown to the correct group of 3 seats by the usher. Each person holds a number stub. What is the probability that each is in the correct seat according to the numbers on seat and stub? A. 1/6 B. 1/4 C. 1/2 D. 1/8

50. From 20 tickets marked with the first 20 numerals, one is drawn at random. What is the chance that it will be a multiple of 3 or of 7? A. 1/2 B. 8/15 C. 3/10 D. 2/5 51. How permutation can be made out of the letters in the world island taking four letters at a time? A. 360 B. 720 C. 120 D. 24 52. How many 4 digit number can be formed without repeating any digit, from the following digit 1,2,3,4 and 6. A. 150 B. 120 C. 140 D. 130 53. How many permutations can made out of the letters of the word ENGINEERING? A. 39,916,800 B. 277,200 C. 55,440 D. 3,326,400 54. How many ways can 3 men and 4 women be seated on a bench if the women to be together? A. 720 B. 576 C. 5040 D. 1024 55. In how many ways can 5 people line up to pay their electric bills? A. 120 B. 1 C. 72 D. 24 56. In how many ways can 5 people line up to pay their electric bills, if two particular persons refuse to follow each other? A. 120 B. 72 C. 90 D. 140

57. How many ways can 7 people be seated at a round table? A. 5040 B. 120 C. 720 D. 840 58. In how many relative orders can we seat 7 people at a round table with a certain people side by side. A. 144 B. 5040 C. 720 D. 1008 59. 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 60. The captain of a baseball team assigns himself to the 4th place in the batting order. In how many ways can he assign the remaining places to his eight teammates if just three men are eligible for the first position? A. 2160 B. 40320 C. 5040 D. 15120 61. In how many ways can PICE chapter with 15 directors choose a president, a vice-president, a secretary, a treasurer, and an auditor, if no member can hold more than one position? A. 630630 B. 3300 C. 5040 D. 15120 62. How many ways can a committee of five be selected from an organization with 35 members? A. 324632 B. 425632 C. 125487 D. 326597 63. How many line segments can be formed by 13 distinct point? A. 156 B. 36 C. 98 D. 78

64. In how many ways can a hostess select six luncheon guests from 10 women if she is to avoid having particular two of them together at the luncheon? A. 210 B. 84 C. 140 D. 168 65. 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? A. 680 B. 840 C. 480 D. 540 66. How many ways can you invite one or more of five friends to a party? A. 25 B. 15 C. 31 D. 62 67. A bag contains 4 red balls, 3 green balls, and 5 blue balls. The probability of not getting a red ball in the first draw is: A. 2 B. 2/3 C. 1 D. 1/3 68. Which of the following cannot be a probability? A. 1 B. 0 C. 1/e D. 0.434343 69. A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black? A. 5/28 B. 5/16 C. 5/32 D. 5/14 70. A bag contains 3 white and 5 red balls. If two balls are drawn at random, find the probability that both are white. A. 3/28 B. 3/8 C. 2/7 D. 5/15

71. In problem 70, find the probability that one ball is white and the other is red. A. 15/56 B. 15/28 C. ¼ D. 225/784 72. In the problem 70, find the probability that all are of the same color. A. 13/30 B. 14/29 C. 13/28 D. 15/28 73. The probability that both stages of a two-stage rocket to function correctly is 0.92. The reliability of the first stage is 0.97. The reliability of the second stage is: A. 0.948 B. 0.958 C. 0.968 D. 0.8924 74. Ricky and George each throw dice. If Ricky gets a sum of four what is the probability that George will get less than of four? A. ½ B. 5/6 C. 9/11 D. 1/12 75. Two fair dice are thrown. What is the probability that the sum of the dice is divisible by 5? A. 7/36 B. 1/9 C. 1/12 D. ¼ 76. An um contains 4 black balls and 6 white balls. What is the probability of getting one black ball and white ball in two consecutive draws from the urn? A. 0.24 B. 0.27 C. 0.53 D. 0.04 77. If three balls in drawn in succession from 5 white and a second bag, find the probability that all are of one color, if the first ball is replaced immediately while the second is not replaced before the third draw. A. 10/121 B. 18/121 C. 28/121 D. 180/14641

78. A first bag contains 5 white balls and 10 black balls. The experiment consists of selecting a bag and then drawing a ball from the selected bag. Find the probability of drawing a white ball. A. 1/3 B. 1/6 C. 1/2 D. 1/8 79. In problem 78, find the probability of drawing a white ball from the first bag. A. 5/6 B. 1/6 C. 2/3 D. 1/3 80. If seven coins are tossed simultaneously, find the probability that will just have three heads. A. 33/128 B. 35/128 C. 30/129 D. 37/129 81. If seven coins are tossed simultaneously, find the probability that there will be at least six tails. A. 2/128 B. 3/128 C. 1/16 D. 2/16 82. A face of a coin is either head or tail. If three coins are tossed, what is are the probability of getting three tails? A. 1/8 B. ½ C. ¼ D. 1/6 83. The face of a coin is either head or tail. If three coins are tossed, what is the probability of getting three tails or three heads? A. 1/8 B. ½ C. ¼ D. 1/6 84. Five fair coins were tossed simultaneously. What is the probability of getting three heads and two tails? A. 1/32 B. 1/16 C. 1/8 D. ¼

85. Throw a fair coin five times. What is the probability of getting three heads and two tails? A. 5/32 B. 5/16 C. 1/32 D. 7/16 86. The probability of getting credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of them got a credit? A. 19/27 B. 8/27 C. 2/3 D. 1/3 87. There are three short questions in mathematics test. For each question, one (1) mark will be awarded for a correct answer and no mark for a wrong answer. If the probability that Mary correctly answers a question in a test is 2/3, determine the probability that Mary gets two marks. A. 4/27 B. 8/27 C. 4/9 D. 2/9 88. A marksman hits 75% of all his targets. What is the probability that he will hit exactly 4 of his next ten shot? A. 0.01622 B. 0.4055 C. 0.004055 D. 0.001622 89. A two-digit number is chosen randomly. What is the probability that it is divisible by 7? A. 7/50 B. 13/90 C. 1/7 D. 7/45 90. One box contains four cards numbered 1, 3,5,and 6. Another box contains three cards numbered 2, 4, and 7. One card is drawn from each bag. Find the probability that the sum is even. A. 5/12 B. 3/7 C. 7/12 D. 5/7

91. Two people are chosen randomly from 4 married couples. What is probability that they are husband and wife? A. 1/28 B. 1/14 C. 3/28 D. 1/7

97. Dennis Rodman sinks 50% of all his attempts. What is the probability that he will make exactly 3 of his next 10 attempts? A. 1/256 B. 3/8 C. 30/128 D. 15/128

92. One letter is taken from each of the words PARALLEL and LEVEL at random. What is the probability of getting the same letter? A. 1/5 B. 1/20 C. 3/20 D. ¾

98. There are 10 defectives per 1000 items of a product in long run. What is the probability that there is one and only one defective in random lot of 100? A. 0.3697 B. 0.3967 C. 0.3796 D. 0.3679

93. In a shooting game, the probability that Botoy and Toto will hit a target is 2/3 and ¾ respectively. What is the probability that the target is hit when both shoot at it once? A. 13/5 B. 5/13 C. 7/12 D. 11/12

99. The UN forces for Bosnia uses a type of missile that hits the target with a probability of 0.3. How many missiles should be fired so that there is at least an 80% probability of hitting the target? A. 2 B. 4 C. 5 D. 3

94. A standard deck of 52 playing cards is well shuffled. The probability that the first four cards dealt from the deck will be four aces is closes to: A. 4 x 10-6 B. 2 x 10-6 C. 3 x 10-6 D. 8 x 10-6

100. In a dice game, one fair is used. The player wins P20.00 if he rolls either 1 or 6. He losses P10.00 if he turns up any other face. What is the expected winning for one roll of the die? A. P40.00 B. P0.00 C. P20.00 D. P10.00

95. A card is chosen from pack of playing cards. What is the probability that it is either red or a picture card? A. 8/13 B. 10/13 C. 19/26 D. 8/15 96. In a poker game consisting of 5 cards, what is the probability of holding 2 aces and 2 Queens? A. 5! /52! B. 5/52 C. 33/54145 D. 1264/45685