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MGF 1106 Summer C 12 Ref: 687619 Review for Exam 4 Mr. Guillen Exam 4 will be on 07/19/12 and cover the following sections: 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 1) Suppose there are 4 roads connecting town A to town B and 3 roads connecting town B to town C. In how many ways can a person travel from A to C via B? 1) 2) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed? 2) 3) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed? 3) 4) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed? 4) 5) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed? 5) 6) How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed? 6) 7) License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed? 7) 8) License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed? 8) 9) At a lumber company that sold shelves, a customer could choose from 4 types of wood, 4 different widths and 5 different lengths. How many different types of shelves could be ordered? 9) 10) How many different three-digit numbers can be written using digits from the set {2, 3, 4, 5, 6} without any repeating digits? 10) 11) A license plate is to consist of 2 letters followed by 5 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted. 11) 12) A license plate is to consist of 2 letters followed by 4 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted. 12) 13) A license plate is to consist of 3 letters followed by 4 digits. Determine the number of different license plates possible if the first letter must be an N , M , or P and repetition of letters and numbers is not permitted. 13) 14) A license plate is to consist of 3 letters followed by 5 digits. Determine the number of different license plates possible if the first letter must be an N , M , or P and repetition of letters and numbers is not permitted. 14) Evaluate the expression. 15) 10P4 15) 16) 6P0 16) 17) 12P8 17) 18) 11P3 18) 19) 9P5 19) 20) 14P5 20) An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. 21) In how many ways can the people be presented? 21) Suppose a traveler wanted to visit a museum, an art gallery, and the state capitol building. 45-minute tours are offered at each attraction hourly from 10 a.m. through 3 p.m. (6 different hours). Solve the problem, disregarding travel time. 22) In how many ways can the traveler visit all three places in one day? 22) 23) In how many ways could the traveler schedule two of the three tours in one day? 23) 24) In how many ways could the traveler schedule all three tours before 1 p.m.? 24) Solve the problem. 25) How many different three-number "combinations" are possible on a combination lock having 23 numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation locks.) 25) 26) There are 9 horses in a race. In how many ways can the first three positions of the order of the finish occur? (Assume there are no ties.) 26) 27) How many ways can the letters in the word "WISCONSIN" be arranged? 27) How many distinguishable permutations of letters are possible in the word? 28) CRITICS 28) 29) LOOK 29) 30) GIGGLE 30) 31) TENNESSEE 31) 32) MISSISSIPPI 32) 33) COMMITTEE 33) Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office. 34) Four representatives 34) 35) Three representatives, if two must be female and one must be male 35) 36) A president, a secretary, and a treasurer, if the president must be a woman and the other two must be men 36) Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these could be hired. 37) Two accounting majors must be hired first, then one economics major, then two marketing 37) majors. Evaluate the expression. 38) 8C5 38) 39) 11C8 39) 40) 9C6 40) 41) 12C7 41) 42) 6C1 42) 43) 10C1 43) 44) 12C7 44) Solve the problem. 45) How many ways can a committee of 2 be selected from a club with 12 members? 45) 46) In how many ways can a student work 6 out of 10 questions on an exam? 46) 47) How many ways can a committee of 4 be selected from a club with 10 members? 47) 48) If the police have 7 suspects, how many different ways can they select 5 for a lineup? 48) 49) In how many ways can a group of 9 students be selected from 10 students? 49) 50) A bag contains 7 apples and 5 oranges. If you select 6 pieces of fruit without looking, how many ways can you get 6 apples? 50) 51) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get 4 oranges? 51) 52) How many 5-card poker hands consisting of 3 aces and 2 kings are possible with an ordinary 52-card deck? 52) 53) Bob is planning to pack 6 shirts and 4 pairs of pants for a trip. If he has 11 shirts and 7 pairs of pants to choose from, in how many different ways can this be done? 53) Of the 2,598,960 different five-card hands possible from a deck of 52 playing cards, how many would contain the following cards? 54) All four kings 54) 55) All red cards 55) 56) No face cards 56) 57) All spades 57) Find the number of ways to get the following card combination from a 52-card deck. 58) Two red cards and three black cards 58) 59) No face cards in a five-card hand 59) 60) Two black queens and two red jacks 60) 61) One spade, two diamonds, and two hearts 61) A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 62) All cherry 62) 63) 2 cherry, 1 lemon 63) 64) All lemon 64) 65) One of each flavor 65) 66) 2 orange, 1 lemon 66) 67) 1 cherry, 2 lemon 67) Solve. 68) A 6-sided die is rolled. What is the probability of rolling a number less than 6? 68) 69) Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 3? 69) 70) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9? 70) Find the probability of the given event. 71) A single fair die is rolled. The number on the die is a 3 or a 5. 71) 72) A single fair die is rolled. The number on the die is greater than 2. 72) 73) A single fair die is rolled. The number on the die is not 6. 73) 74) A single fair die is rolled. The number on the die is a multiple of 3. 74) 75) A single fair die is rolled. The number on the die is prime. 75) 76) Two fair dice are rolled. The sum of the numbers on the dice is 5. 76) 77) Two fair dice are rolled. The sum of the numbers on the dice is 6 or 10. 77) 78) Two fair dice are rolled. The sum of the numbers on the dice is greater than 10. 78) Find the probability. 79) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting a king. 79) 80) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting a black 7. 80) 81) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting a club. 81) 82) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting the 4 of hearts. 82) 83) When a single card is drawn from a well-shuffled 52-card deck, find the probability of getting a black 5 or a black 4. 83) 84) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 7? 84) 85) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 6? 85) 86) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a heart, club, or diamond? 86) 87) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a black card that is not a face card? 87) 88) A bag contains 4 red marbles, 7 blue marbles, and 2 green marbles. What is the probability that a randomly selected marble is blue? 88) 89) A lottery game has balls numbered 1 through 15. What is the probability that a randomly selected ball is an even numbered ball or a 12? 89) 90) A bag contains 7 red marbles, 2 blue marbles, and 1 green marble. What is the probability that a randomly selected marble is not blue? 90) Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. 91) In bridge, exactly 3 kings and exactly 3 queens 91) 92) In bridge, 4 aces 92) 93) In bridge, all cards in one suit 93) Find the odds. 94) 94) What are the odds of drawing a 3 from these cards? 95) 95) What are the odds of drawing an even number from these cards? 96) 96) What are the odds of drawing a number greater than 2 from these cards? 97) A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for the cube showing an odd number? 97) 98) A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for the cube showing a 4? 98) 99) A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds for the cube showing a number less than 3? 99) 100) The kings are separated from a deck of standard playing cards and shuffled. One is randomly selected. What are the odds in favor of drawing a black card? 100) 101) Seven slips of paper marked with the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in a box and mixed well. Two are drawn. What are the odds that the sum of the numbers on the two selected slips is not 5? Solve the problem. 102) The odds in favor of a horse winning a race are posted as 9 : 2. Find the probability that the horse will win the race. 101) 102) 103) The odds in favor of a horse winning a race are posted as 7 : 5. Find the probability that the horse will lose the race. 103) 104) The odds in favor of Carl beating his friend in a round of golf are 7 : 4 Find the probability that Carl will beat his friend. 104) 105) The odds in favor of Carl beating his friend in a round of golf are 3 : 2. Find the probability that Carl will lose. 105) 106) The odds against Carl beating his friend in a round of golf are 4 : 3. Find the probability that Carl will beat his friend. 106) 107) The odds against Carl beating his friend in a round of golf are 9 : 7. Find the probability that Carl will lose. 107) 108) The odds in favor of Jerome beating his friend in a round of golf are 1 : 5. Find the probability that Jerome will beat his friend. 108) 109) The odds in favor of Trudy beating her friend in a round of golf are 1 : 8. Find the probability that Trudy will lose. 109) 110) The odds against Chip beating his friend in a round of golf are 1 : 9. Find the probability that Chip will beat his friend. 110) 111) The odds against Muffy beating her friend in a round of golf are 1 : 4. Find the probability that Muffy will lose. 111) 112) If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade. 112) 113) If two cards are drawn without replacement from a deck, find the probability that the second card is red, given that the first card was a heart. 113) 114) If two cards are drawn without replacement from a deck, find the probability that the second card is a face card, given that the first card was a queen. 114) 115) If two cards are drawn without replacement from a deck, find the probability that the second card is an ace, given that the first card was an ace. 115) 116) If three cards are drawn without replacement from a deck, find the probability that the third card is a heart, given that the first two cards were hearts. 116) 117) If three cards are drawn without replacement from a deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5. 117) Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability. 118) The second marble is red given the first marble is white. 118) 119) The second marble is white given the first marble is blue. 119) 120) The second marble is blue given the first marble is white. 120) 121) The second marble is blue given the first marble is red. 121) 122) The second marble is blue given the first marble is blue. 122) Answer Key Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 12 ways 10,000 four-digit numbers 210 three-digit numbers 210 three-digit numbers 10,000 four-digit numbers 2520 five-digit numbers 67,600 plates 67,600 plates 80 types 60 three-digit numbers 19,656,000 3,276,000 9,072,000 54,432,000 5040 1 19,958,400 990 15,120 240,240 5,040 120 30 6 10,626 three-number "combinations" 504 45,360 1260 12 120 3780 34,650 45,360 120 6 12 144 ways 56 165 84 792 6 10 792 66 ways 210 ways 210 ways 21 ways 10 ways 7 ways 0 ways Answer Key Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW 52) 53) 54) 55) 56) 57) 58) 59) 60) 61) 62) 63) 64) 65) 66) 67) 24 five-card hands 16,170 48 hands 65,780 hands 658,008 hands 1287 hands 845,000 ways 658,008 ways 48 ways 79,092 ways .1212 .1818 0 .2182 .0364 .0364 5 68) 6 69) 1 18 70) 1 6 71) 1 3 72) 2 3 73) 5 6 74) 1 3 75) 1 2 76) 1 9 77) 2 9 78) 1 12 79) 1 13 80) 1 26 81) 1 4 82) 1 52 Answer Key Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW 83) 1 13 84) 2 13 85) 4 13 86) 3 4 87) 5 13 88) 7 13 89) 7 15 90) 4 5 91) .00097 92) .00264 6.30 x 10-12 1:4 2:3 3:2 1:1 1:5 1:2 1 to 1 19 to 2 9 102) 11 93) 94) 95) 96) 97) 98) 99) 100) 101) 103) 5 12 104) 7 11 105) 2 5 106) 3 7 107) 9 16 108) 1 6 109) 8 9 110) 9 10 Answer Key Testname: MGF_1106_SUMMER_C_EXAM_4_REVIEW 111) 1 5 112) 4 17 113) 25 51 114) 11 51 115) 1 17 116) 11 50 117) 11 50 118) 2 7 119) 3 7 120) 1 7 121) 1 7 122) 0 ��������������������������������������������������������������������������� ��������������������������������������������������������������������������������� �����������������������������������������������������