# Algebra II- Chapter 12- Test Review

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1 Sections: Counting Principle Permutations Combinations Probability Name Choose the letter of the term that best matches each statement or phrase. 1. An illustration used to show the total number of A. circular permutations possible outcomes. B. combination 2. The number of possibilities of n objects, taken r at n! a time and defined as C(n, r) = ( n r)! r! C. fundamental counting principle 3. The number of ways that n objects can be arranged in a circle and defined by (n 1)! D. linear permutation 4. If one event can occur in m ways and another in n E. odds ways, then the number of ways that both can occur is m n ways f. success 5. The desired outcome of an event g. tree diagram 6. The number of possibilities of n objects arranged in a line and defined by P(n, r) = ( n r)! 7. The ratio of the number of ways an event can succeed to the number of ways it can fail n! How many ways can the letters of each word be arranged. 8. MONDAY 9. MOM 10. STEREO Determine whether each situation involves a permutation or a combination. 11. choosing a class president, vice president, and secretary 12. four tennis players from a group of nine 13. eight toppings for ice cream State the probability of an event occurring, given the odds of the event : : : : : :1 Evaluate each expression C C C ( 9 C 3 )( 6 C 2 )

2 Solve. 24. The letters A, B, C, and D are used to form four-letter passwords for entering a computer file. How many passwords are possible if letters can be repeated any number of times? 25. In a bag there are 5 math questions and 4 science questions. Ardie picks a question from the bag. What are the odds of not picking a science question? 26. How many 4-person bobsled teams can be chosen from a group of 9 athletes? 27. How many 4-digit positive even integers are there? 28. Ten points lie on a circle. How many line segments can be drawn between any two points? 29. How many different ways can 4 different books be arranged on the shelf? 30. How many 5-sided polygons can be formed by joining any 5 of 11 points located on a circle? 31. A school club has 15 boys and 16 girls. How many different 6 person committees can be selected from the membership if equal numbers of boys and girls are to be selected? 32. How many diagonals does a polygon with 12 sides have? 33. An urn contains 8 white balls numbered 1 through 8, 6 blue balls numbered 1 through 6, and 9 red balls numbered 1 through 9. How many distinct groups of 6 balls can be selected to meet each condition? a.) All balls are red b.) Three are blue, 2 are white, and 1 is red c.) Two are blue, and 4 are red d.) Exactly 4 balls are white 34. How many ways can 8 members of a family be seated side-by-side in a movie theater if the father is seated in the aisle seat?

3 35. What are the odds that a person chosen at random got a passing grade on an algebra test if the scores were 3 A s, 4 B s, 10 C s, 2 D s and 2 F s? 36. How many ways can the first five letters of the alphabet be arranged if each is used only once? 37. How many license plate numbers consisting of three letters followed by three numbers are possible when repetition is allowed? 38. How many license plates are possible using the information in problem 37 if no repetition is allowed? 39. From a dessert cart in a fine restaurant, customers are allowed to pick 3 desserts from the 10 that are displayed. How many combinations are possible? 40. How many ways can 3 books be arranged on a shelf if chosen from a selection of 7 different books? 41. A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals could be ordered if each has a main dish, a salad, and a dessert? 42. One bag of candy gummy fish contains 15 red gummy fish, 10 yellow gummy fish, and 6 green gummy fish. Find the probability of each selection. a.) picking a red gummy fish b.) not picking a yellow gummy fish c.) picking a green gummy fish d.) not picking a red gummy fish 43. How many 5-digit even numbers can be formed using the digits 4,6,7,2,8 if digits can be repeated any number of times? 44. How many ways can 8 campers be seated around a campfire? 45. State the odds of an event occurring, given the probability of the event. a.) b.) 3 5 c.) 99 1 d.) 1000 e.) f.) In a group of 10 people, each person shakes hands with everyone else once. How many handshakes are there? (this is a famous problem)

4 47. For next year s schedule of classes, mathematics, English, history and science are scheduled during the first four period of the day. Your schedule is randomly selected by a computer. Find the probability that English, math, science and history will be scheduled in that order. 48. Seven letters are chosen, one at a time, at random from those in the word ENGLISH. a.) Find the probability that they will be chosen in alphabetical order. b.) Find the probability that the first letter will be a vowel. 49. Consider a state lottery which randomly selects 6 numbered balls from a bin. The balls are numbered from 1 to 52. To win the jackpot, a player must match all 6 balls, in any order. Determine the probability of winning the jackpot (matching all 6 numbers) for a person who buys one ticket. 50. To increase the difficulty of the lottery (and also the size of the jackpot), the state decides to label the last ball which is drawn as the Final Ball. To win the jackpot, a ticket must match the first five balls in any order, and the Final Ball. Determine the probability of winning the jackpot for a person who buys one ticket.

5 Create Pascal s Triangle Below: Use the binomial theorem to write the binomial expansion. 51.) ( x 10 ) 5 52.) (x + 3y) 7

6 53.) Find the indicated probability. State whether A and B are mutually exclusive. ( ) ( ) ( B) = ( and B) 54. P A = P B = 0.55 P A or 0.85 P A = ( ) = 40% ( ) = ( B) = ( B) P A P B P A or 60% P A and = 12% Mutually exclusive: Mutually exclusive: Find P(A ) 56. P A ( ) = 1 5 P( A' ) = Choosing Cards For problems 4 through 7: ONE card is randomly drawn from a standard 52-card deck. Find the probability of the given event. State your answer in fractions. 57. An queen or a heart = 58. A face card and a club = 59. Not an ace = 60. Less than or equal to four (an ace is one) = 61. You randomly select two cards from a standard deck of 52 cards. What is the probability that the first card that you select is a jack or an ace and the second card is an ace, jack, or queen if you replace the first card before selecting the second? State your answer in rounded to four decimals.

7 62. In exercise 61, what is the probability if you DO NOT replace the first card before selecting the second? State your answer in rounded to four decimals. 63. The probability of a tourist visiting an area cave is.70 and of a tourist visiting a nearby park is.60. The probability of visiting both places on the same day is.40. The probability that a tourist visits an area cave or a nearby park on the same day is: 64. A drawer contains 7 pairs of white socks and 4 pairs of gray socks. You randomly select 3 pairs of socks from the drawer. Find the probability that the 3 pairs that you selected are white. Round your answer to three decimals. Use the below information for problems Marbles in a jar - A jar contains 12 red marbles, 16 blue marbles, and 18 white marbles. Find the probability of choosing the given marbles from the jar. Answer with decimals rounded to 3 places. Part a) With replacement Part b) Without replacement 65. red, then blue 66. white, then white 67. red, then white, then red 65 a) 66 a) 67 a) b) b) b) 68. Angela usually rushes to make it to the bus stop in time to catch the school bus, and will often miss the bus if it is early. The bus comes early to Angela s stop 28% of the time. What is the probability that the bus will come early at least once during a 5 day school week? 69. A tennis player wins a match 55% of the time when she serves first and 47% of the time when her opponents serves first. The player who serves first is determined by a coin toss before the match. What is the probability that the player wins a given match?

8 70. A card is drawn randomly from a standard 52-card deck. Find the probability of drawing a red face card. 71. A school club has 5 freshman, 3 sophomores, 2 seniors and 2 juniors. How many different 8 person committees can be formed if equal numbers of freshman, sophomores, juniors and seniors are to be selected? 72. If the probability of an event occurring is 8 25, what are the odds that the event will occur? 73. If the odds of winning a contest are 1:553, what is the probability of losing the contest? 74. A coin purse contains 5 pennies, 7 nickels, and 8 dimes. A coin is selected at random. Find the probability that the coin is a dime. 75. Penn State University holds a lottery for spaces in their dormitories for sophomores. They have a total of 1,580 rooms available for sophomores. If you are one of 2,348 students entering the lottery for a dormitory room, what are the odds that you will have to look elsewhere for housing? 76. In a game of Go Fish you choose 1 card from player to your right. Your hand contains: K Q The player to your right is holding: J A When you draw one card from the person to your right without seeing his cards, what is the probability that you will create a pair in your hand? (A pair consists of two cards that are the same number/face card).

9 77. The table at right gives the results of rolling one die 50 times. What is the experimental probability of rolling a 3? Roll Number of occurrences The target at right is used for a game of darts. The inner circle has a radius of 1 and each ring has a radius width of 1. If a dart has the same chance of landing at any point in the square, what is the probability of landing your first dart in either of the rings worth 30 or 40 points? " 12" 79. A bag of Hershey kisses contains 3 milk chocolate, 10 dark chocolate, and 15 chocolate almond kisses. What is the probability of drawing a milk chocolate or a dark chocolate kiss? 80. Use the data to complete the problem BY HAND, show all your work for full credit! 46, 18, 64, 28, 48, 18 MEAN: MEDIAN: MODE: RANGE: VARIANCE: STANDARD DEV: Min: Q 1 : Q 2 : Q 3 : Max: IQR: Use the information you just found to draw a box-and-whisker plot

10 81. The following statistics were produced at the end of a week at a weight loss center indicating pounds lost. mean = 5 lbs. median = 7 lbs. mode = 4 lbs. first quartile = 2 lbs. third quartile = 8.5 lbs. standard deviation = 0.5 lbs. Which of the following statements are correct? I. One quarter of weight watchers lost 2 pounds or less II. The middle 50% of the weight watchers lost between 2 and 8.5 pounds III. The most common weight loss was 4 pounds. (A) I only (B) II only (C) III only (D) II and III only (E) I, II and III 82. The boxplots above summarize two sets of data, A and B. Which of the following must be true? I. Set B contains more observations than Set A II. Set A has a larger range than Set B III. Set A and Set B have the same median. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II and III

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