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Geometry & Probability 8 Room 245 Class: Name: Date: Homework for: Unit 3 Probability Probability Guiding Concepts In this unit, you will investigate chance processes and develop, use, and evaluate probability models. At the end of the unit, you should be able to: Understand that the probability of a chance event is a number between 0 and 1. Compare probabilities from a model to observe frequencies. Approximate or predict the probability of a chance event by collecting data and observing the frequency of the event. Develop a probability model and use it to find probabilities of events. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Selected answers 1b. ¼ 17. 1d. 0 3. 0/10, 3/10, 1/10, 3/10, 1/5 19. 4. each has 1/6 probability 6. 37 goals 7a. 300 7b. 9. 1/26 43. 5/12 49. no 51. 2/13 53. ½ 59. 80% 61. 12/13 63. 11/13 9,000,000 21. 6,344,000 fewer 27a. 30 27b. 336 29. 41. 180, appetizer combination 32. 5,985 39. 1/36 400 1/3 2 Geometry & Probability 8 Room 245 Class-BiN: Name: Date: - Introduction to Probability 1. A jar contains 6 red, 8 blue, one white, 7 black, and two yellow marbles. 2. A spinner is divided into 8 sections of equal size. The sections are numbered 1 through 8. Use this information to determine the probability of selecting: Use this information to determine the probability of the needle landing on: a. a white marble a. section 7 b. a red marble b. an even numbered section c. a yellow marble c. section 1, 2, 3, or 4 d. a purple marble d. section 9 e. a black marble e. section 8 3 Experimental and Theoretical Probability 3. A die is rolled 10 times and the outcomes are: 4. A die is rolled. Complete the table. Outcome Number of Times Roll 1 0 Roll 2 3 Roll 3 1 Roll 4 3 Roll 5 2 Roll 6 1 Roll Theoretical Probability 1 2 3 4 5 6 List the experimental probability for rolling a: Roll Experimental Probability 1 2 3 4 5 4 Geometry & Probability 8 Room 245 5. A spinner contains 8 equally divided sections, two sections have the letter A, 3 sections have the letter B, one section has the letter C, one section has the D, and one section has the letter E. Draw a picture of the spinner Use your drawing to fill in the chart Spin Theoretical Probability A Class: Name: Date: The spinner is spun 10 times and the outcomes are: Outcome Number of Times A 4 B 1 C 3 D 2 E 0 List the experimental probability for spinning a: Spin B C D E A B C E Experimental Probability Word Problems 8. A die is rolled. What is the theoretical probability for rolling a 3? 6. You made 8 out of 15 shots on goal. Use experimental probability to predict how many goals you will make tomorrow if you take 70 shots. 9. Mary rolls a die six times and rolls a 3 on two of the rolls. What is the experimental probability for rolling a 3? 7. There are 1000 buttons in the jar. You randomly select 10 buttons and get 3 red, 4 blue, 2 white, and 1 black. Use experimental probability to predict how many buttons in the jar are: 10. Create a situation where the experimental probability and the theoretical probability have the same value. a. Red b. Blue c. White d. Black 6 Geometry & Probability 8 Room 245 11. A coin is flipped. a. What is the theoretical probability for flipping a tail? b. Mark and John flip a coin twenty times and get 8 heads, 12 tails. What is the experimental probability for flipping a tail? c. If Mark & John flip the coin 100 times, what do you think will happen to the experimental probability? 12. Bart makes 20% of his free throws. a. If he takes 500 free throws, how many go in the basket? b. Predict how many baskets Bart makes when he takes 25 free throws. Class: Name: Date: 13. A factory produces 1000 light bulbs per minute. Each minute, one bulb produced will be defective. a. What is the theoretical probability of selecting the defective bulb from the light bulbs produced in one minute? b. What is the theoretical probability of selecting a defective bulb from the light bulbs produced in one hour? 14. Every 100th box of candy contains a prize. a. What is the theoretical probability for selecting the box of candy with a prize? Fundamental Counting Principle continued from #22… b. A case contains 1000 boxes and how many prizes? 17. A restaurant has 4 appetizers, 9 entrees, and 5 dessert choices. a. How many meals are possible? c. What is the probability of selecting a box containing a prize a case? b. If the restaurant wants to increase their meals as much as possible by adding one more item, should they add an appetizer, an entrée or a dessert? 15. Create a situation where the experimental probability is greater than the theoretical probability. 18. Martha has 8 shirts, 6 pair of pants, and 4 different pair of shoes. Assuming everything matches, how many days can Martha go without wearing the same outfit? 16. How does understanding probability help someone who plays cards? 8 Geometry & Probability 8 Room 245 19. How many different 7 digit telephone numbers are there, if the first digit cannot be 0? 20. By adding an area code to each 7-digit telephone number, the phone company increased the amount of telephone numbers by how many? (Remember that the first digit in the area code and the phone number itself cannot be 0.) Class: Name: Date: 21. One state is considering creating license plates where letters cannot be repeated. If the state has license plates consisting of three letters, followed by three different digits, how many fewer license plates are available when repetition of letters is not allowed? 22. A phone comes in 12 different colors, 5 different headsets, and 7 different styles. How many different phones are available? 23. Mark is taking a 10 question, True/False quiz. How many different ways can the quiz be answered? 25. Frank is calling his sister and can’t remember the first two digits of her phone number. He remembers the remaining five digits. What is the greatest number of attempts that Frank would have to make to complete the call? (He knows that the first digit of his sister’s phone number is not 0.) 24. A combination lock has a combination of 5 single digits, none of which are repeated. How many different combinations are there? 26. A pizza parlor provides customers with the opportunity to create their own single topping pizza by selecting from 4 different crusts, 5 different sauces, 3 different cheeses, and 15 different toppings. a. How many pizzas are possible? b. If a second different topping choice is allowed, how many pizzas are possible? 10 Geometry & Probability 8 Room 245 Class-BiN: Name: Date: - Permutations and Combinations 27. Find the value of the following: a. 6P2 30. You must fit 10 out of 15 dogs in the cages along the wall (one dog per cage). How many different ways are there to place them in the cages? This is an example of a ________________________. b. 8P3 c. 10P2 31. Find the value of the following: a. 6C4 d. 3P3 b. 5C1 28. Thirty dogs and their handlers enter a show ring. The judge will pick 5 dogs to place in the contest. How many different ways can the first, second, third, fourth, and fifth place be awarded? c. 4C4 d. 6C2 32. There are 21 girls on a soccer team. Four of these girls will be picked to be on the AllAmerican Team. How many different groups of players can be chosen? 29. You create a sundae with 3 out of 10 flavors at the Ice Cream Store. This is an example of a ________________________. 11 33. Find the value of the following: a. 10P6 36. Your parents inform you that you can only invite 30 people out of the 50 people that you wanted to invite to your party. The possibilities of the people you can invite is an example of a ________________________. b. 9P4 c. 5P5 37. Find the value of the following: a. 10C8 d. 4P1 b. 4C2 34. Twenty snowboarders enter a race. The top 4 will get medals. How many different ways can the first, second, third, and fourth medals be given? c. 6C5 d. 3C3 38. There are 20 children in a kindergarten class. Five of these children will be picked for the outstanding kindergarten award. How many different groups of kindergarteners can be chosen? 35. You must buy 3 kinds of soda out of 8 at the store. This is an example of a ________________________. 12 Geometry & Probability 8 Room 245 Class: Name: Date: Probability of Compound Events 39. You are given a pair of dice. One die is numbered 1 through 6 but the other die is numbered 7 through 12. What are the odds of rolling a 3 and an 8? 40. A machine generates numbers randomly from balls numbered 5 through 15. Two balls are selected, with replacement. What are the odds that both the numbers picked will be 8? 41. A bag with 6 blue marbles, 3 green marbles, and 4 orange marbles is lying on a table. What is the probability that John will pick 2 green marbles? (without replacement) 42. What is the probability that the first three cards drawn from a full deck of cards are clubs? (without replacement) 43. There are 6 male puppies and 3 female puppies. What is the probability that the first two puppies chosen will be males? (without replacement) 44. What is the probability that the first three cards drawn from a full deck of cards are kings? 47. A lottery machine generates numbers randomly. Three numbers are picked from 1 and 20. What is the probability that all three numbers that are picked are 17? 45. You dropped two coins. What is the probability that they will both land on heads? 48. There are 4 blue marbles and 2 red marbles. A marble is selected and not returned. What is the probability that two red marbles will be chosen? 46. Bill Gates wrote a computer program that generates three random numbers from 1 and 10. What is the probability that all three values will be three? 14 Geometry & Probability 8 Room 245 Class: Name: Date: Probabilities of Mutually Exclusive and Overlapping Events 49. Are these events mutually exclusive? 52. P(rolling a 2 or a 6) on a die Event A: Roll an even number Event B: Roll a prime number 50. Are these events mutually exclusive? 53. P(rolling a 2 or an even number) on a die Event A: Select a bird Event B: Select a bald eagle 54. Are these events mutually exclusive? Calculate: 51. P(selecting a queen or a 10) from a deck of cards Event A: Roll a number greater than 2 Event B: Roll a number less than 3 55. Are these events mutually exclusive? 57. P(rolling an odd number or a number greater than 3) on a die Event A: Select a consonant from the alphabet Event B: Select a vowel from the alphabet 58. P(choosing a club or a black card) from a deck of cards Calculate: 56. P(choosing a 4 or a jack) from a deck of cards 16 Geometry & Probability 8 Room 245 Class: Name: Date: Complementary Events 59. P(snow) = 20% 64. P(no snow) = 60. P(A) = 0.9 P(not A) = 61. What is the probability of not selecting a queen from a deck of cards? 62. What is the probability of not rolling a 1 on a die? 63. What is the probability of not selecting a queen or a king from a full deck of cards? P(rain) = 5% P(no rain) = 65. P(A) = 3/5 P(not A) = 66. What is the probability of not selecting a four from a deck of cards? 67. What is the probability of not rolling a 6 on a die? 68. If 22% of the people in the room are bald, what percent are not bald?