12.1 Practice A. Name Date. In Exercises 1 and 2, find the number of possible outcomes in the sample space. Then list the possible outcomes.

Transcription

1 Name Date 12.1 Practice A In Exercises 1 and 2, find the number of possible outcomes in the sample space. Then list the possible outcomes. 1. You flip three coins. 2. A clown has three purple balloons labeled a, b, and c, three yellow balloons labeled a, b, and c, and three turquoise balloons labeled a, b, and c. The clown chooses a balloon at random. 3. Your friend has eight sweatshirts. Three sweatshirts are green, one is white, and four are blue. You forgot your sweatshirt, so your friend is going to bring one for you as well as one for himself. What is the probability that your friend will bring two blue sweatshirts? 4. The estimated percentage student GPA distribution is shown. Find the probability of each event. GPA Distribution : 12% : 7%,1.0: 6% : 9% : 25% : 41% a. A student chosen at random has GPA of at least 3.0. b. A student chosen at random has GPA between 1.0 and 2.9, inclusive. 5. A bag contains the same number of each of four different colors of marbles. A marble is drawn, its color is recorded, and then the marble is placed back in the bag. This process is repeated until 40 marbles have been drawn. The table shows the results. For which marble is the experimental probability of drawing the marble the same as the theoretical probability? Drawing Results yellow red blue black Geometry Copyright Big Ideas Learning, LLC

2 Name Date 12.1 Practice B In Exercises 1 and 2, find the number of possible outcomes in the sample space. Then list the possible outcomes. 1. You roll a die and draw a token at random from a bag containing three pink tokens and one red token. 2. You draw 3 marbles without replacement from a bag containing two brown marbles and three yellow marbles. 3. When two six-sided dice are rolled, there are 36 possible outcomes. a. Find the probability that the sum is 5. b. Find the probability that the sum is not 5. c. Find the probability that the sum is less than or equal to 5. d. Find the probability that the sum is less than A tire is hung from a tree. The outside diameter is 34 inches and the inside diameter is 14 inches. You throw a baseball toward the opening of the tire. Your baseball is equally likely to hit any point on the tire or in the opening of the tire. What is the probability that you will throw the baseball through the opening in the tire? In Exercises 5 7, tell whether the statement is always, sometimes, or never true. Explain your reasoning. 5. If there are exactly five possible outcomes and all outcomes are equally likely, then the theoretical probability of any of the five outcomes occurring is The experimental probability of an event occurring is equal to the theoretical probability of an event occurring. 7. The probability of an event added to the probability of the complement of the event is equal to A manufacturer tests 900 dishwashers and finds that 24 of them are defective. Find the probability that a dishwasher chosen at random has a defect. An apartment building orders 40 of the dishwashers. Predict the number of dishwashers in the apartment with defects. Copyright Big Ideas Learning, LLC Geometry 423

3 Name Date 12.2 Practice A In Exercises 1 and 2, tell whether the events are independent or dependent. Explain your reasoning. 1. A box contains an assortment of tool items on clearance. You randomly choose a sale item, look at it, and then put it back in the box. Then you randomly choose another sale item. Event A: You choose a hammer first. Event B: You choose a pair of pliers second. 2. A cooler contains an assortment of juice boxes. You randomly choose a juice box and drink it. Then you randomly choose another juice box. Event A: You choose an orange juice box first. Event B: You choose a grape juice box second. In Exercises 3 and 4, determine whether the events are independent. 3. You are playing a game that requires rolling a die twice. Use a sample space to determine whether rolling a 2 and then a 6 are independent events. 4. A game show host picks contestants for the next game, from an audience of 150. The host randomly chooses a thirty year old, and then randomly chooses a nineteen year old. Use a sample space to determine whether randomly choosing a thirty year old first and randomly selecting a nineteen year old second are independent events. 5. A hat contains 10 pieces of paper numbered from 1 to 10. Find the probability of each pair of events occurring as described. a. You randomly choose the number 1, you replace the number, and then you randomly choose the number 10. b. You randomly choose the number 5, you do not replace the number, and then you randomly choose the number The probability that a stock increases in value on a Monday is 60%. When the stock increases in value on Monday, the probability that the stock increases in value on Tuesday is 80%. What is the probability that the stock increases in value on both Monday and Tuesday of a given week? Copyright Big Ideas Learning, LLC Geometry 427

4 Name Date 12.2 Practice B In Exercises 1 and 2, tell whether the events are independent or dependent. Explain your reasoning. 1. You and a friend are picking teams for a softball game. You randomly choose a player. Then your friend randomly chooses a player. Event A: You choose a pitcher. Event B: Your friend chooses a first baseman. 2. You are making bracelets for party favors. You randomly choose a charm and a piece of leather. Event A: You choose heart-shaped charm first. Event B: You choose a brown piece of leather second. In Exercises 3 and 4, determine whether the events are independent. 3. You are playing a game that requires flipping a coin twice. Use a sample space to determine whether flipping heads and then tails are independent events. 4. A game show host picks contestants for the next game from an audience of 5 females and 4 males. The host randomly chooses a male, and then randomly chooses a male. Use a sample space to determine whether randomly choosing a male first and randomly choosing a male second are independent events. 5. A sack contains the 26 letters of the alphabet, each printed on a separate wooden tile. You randomly draw one letter, and then you randomly draw a second letter. Find the probability of each pair of events. a. You replace the first letter before drawing the second letter. Event A: The first letter drawn is T. Event B: The second letter drawn is A. b. You do not replace the first letter tile before drawing the second letter tile. Event A: The first letter drawn is P. Event B: The second letter drawn is S. 6. At a high school football game, 80% of the spectators buy a beverage at the concession stand. Only 20% of the spectators buy both a beverage and a food item. What is the probability that a spectator who buys a beverage also buys a food item? 428 Geometry Copyright Big Ideas Learning, LLC

5 Name Date 12.3 Practice A In Exercises 1 and 2, complete the two-way table. 1. Role Ran a Half Marathon Yes No Total Student Teacher 7 Total Owns Dog Yes No Total Owns Cat Yes No 107 Total In a survey, 112 people feel that the amount of fresh water allowed to empty into the salt water river should be reduced, and 87 people did not feel that the amount of fresh water allowed to empty into the salt water river should be reduced. Of those who feel that the amount of fresh water released should be reduced, 98 people fish the salt water river. Of those that do not feel that the amount of fresh water released should be reduced, 12 people fish the salt water river. a. Organize these results in a two-way table. Then find and interpret the marginal frequencies. b. Make a two-way table that shows the joint and marginal relative frequencies. c. Make a two-way table that shows the conditional relative frequencies for each fish category. 432 Geometry Copyright Big Ideas Learning, LLC

6 Name Date 12.3 Practice B In Exercises 1 and 2, use the two-way table to create another two-way table that shows the joint and marginal relative frequencies. 1. Surfing Style Regular Advanced Total Gender Male Female Total Fishing License Yes No Total Hunting License Yes No Total In a survey, 5 people exercise regularly and 21 people do not. Of those who exercise regularly, 1 person felt tired. Of those that did not exercise regularly, 1 person felt tired. a. Organize these results in a two-way table. Then find and interpret the marginal frequencies. b. Make a two-way table that shows the joint and marginal relative frequencies. c. Make a two-way table that shows the conditional relative frequencies for each exercise category. Copyright Big Ideas Learning, LLC Geometry 433

7 Name Date 12.4 Practice A In Exercises 1 and 2, events A and B are disjoint. Find P(A or B). = 1 = PA ( ) = 0.4, PB ( ) = PA ( ), PB ( ) 3. At the high school swim meet, you and your friend are competing in the 50 Freestyle event. You estimate that there is a 40% chance you will win and a 35% chance your friend will win. What is the probability that you or your friend will win the 50 Freestyle event? In Exercises 4 and 5, you roll a die. Find P(A or B). 4. Event A: Roll a Event A: Roll an even number. Event B: Roll an odd number. Event B: Roll a number greater than You bring your cat to the veterinarian for her yearly check-up. The veterinarian tells you that there is a 75% probability that your cat has a kidney disorder or is diabetic, with a 40% chance it has a kidney disorder and a 50% chance it is diabetic. What is the probability that your cat has both a kidney disorder and is diabetic? 7. A game show has three doors. A Grand Prize is behind one of the doors, a Nice Prize is behind one of the doors, and a Dummy Prize is behind one of the doors. You have been watching the show for a while and the table gives your estimates of the probabilities for the given scenarios. Door 1 Door 2 Door 3 Grand Prize Nice Prize Dummy Prize a. Find the probability that you win either the Grand Prize or a Nice Prize if you choose Door 1. b. Find the probability that you win either the Grand Prize or a Nice Prize if you choose Door 2. c. Find the probability that you win either the Grand Prize or a Nice Prize if you choose Door 3. d. Which door should you choose? Explain. Copyright Big Ideas Learning, LLC Geometry 437

8 Name Date 12.4 Practice B In Exercises 1 and 2, events A and B are disjoint. Find P(A or B). = 1 = PA ( ) = 0.375, PB ( ) = PA ( ), PB ( ) 3. You are performing an experiment to determine how well pineapple plants grow in different soils. Out of the 40 pineapple plants, 16 are planted in sandy soil, 18 are planted in potting soil, and 7 are planted in a mixture of sandy soil and potting soil. What is the probability that a pineapple plant in the experiment is planted in sandy soil or potting soil? In Exercises 4 and 5, you roll a die. Find P(A or B). 4. Event A: Roll a prime number. 5. Event A: Roll an even number. Event B: Roll a number greater than 2. Event B: Roll an odd number. 6. An Educational Advisor estimates that there is a 90% probability that a freshman college student will take either a mathematics class or an English class, with an 80% probability that the student will take a mathematics class and a 75% probability that the student will take an English class. What is the probability that a freshman college student will take both a mathematics class and an English class? 7. A test diagnoses a disease correctly 92% of the time when a person has the disease and 80% of the time when the person does not have the disease. Approximately 4% of people in the United States have the disease. Fill in the probabilities along the branches of the probability tree diagram and then determine the probability that a randomly selected person is correctly diagnosed by the test. Population of United States Event A: Person has the disease. Event A: Person does not have the disease. Event B: Correct diagnosis. Event B: Incorrect diagnosis. Event B: Correct diagnosis. Event B: Incorrect diagnosis. 438 Geometry Copyright Big Ideas Learning, LLC

9 Name Date 12.5 Practice A In Exercises 1 3, find the number of ways that you can arrange (a) all of the letters and (b) 2 of the letters in the given word. 1. HAT 2. PORT 3. CHURN In Exercises 4 9, evaluate the expression. 4. 4P P P P P P Fifteen sailboats are racing in a regatta. In how many different ways can three sailboats finish first, second, and third? 11. Your bowling team and your friend s bowling team are in a league with 6 other teams. In tonight s competition, find the probability that your friend s team finishes first and your team finishes second. In Exercises 12 and 13, count the possible combinations of r letters chosen from the given list. 12. H, I, J, K, L; r = U, V, W, X, Y; r = 2 In Exercises 14 19, evaluate the expression C C C C C C You and your friends are ordering a 3-topping pizza. The pizzeria offers 8 different pizza toppings. How many combinations of 3 pizza toppings are possible? In Exercises 21 and 22, tell whether the question can be answered using permutations or combinations. Explain your reasoning. Then answer the question. 21. On a biology lab exam, there are 8 stations available. You must complete the labs at 6 of the 8 stations. In how many ways can you complete the exam? 22. Your committee is voting on their logo. There are 7 possible logos and you are to rank your top 3 logos. In how many ways can you rank your top 3 logos? 442 Geometry Copyright Big Ideas Learning, LLC

10 Name Date 12.5 Practice B In Exercises 1 3, find the number of ways that you can arrange (a) all of the letters and (b) 2 of the letters in the given word. 1. SMILE 2. POLITE 3. WONDERFUL In Exercises 4 9, evaluate the expression. 4. 6P P P P P P You have textbooks for 7 different classes. In how many different ways can you arrange them together on your bookshelf? 11. You make wristbands for Team Spirit Week. Each wristband has a bead containing a letter of the word COLTS. You randomly draw one of the 8 beads from a cup. Find the probability that COLTS is spelled correctly when you draw the beads. In Exercises 12 and 13, count the possible combinations of r letters chosen from the given list. 12. P, Q, R, S, T, U; r = G, H, I, J, K, L; r = 4 In Exercises 14 19, evaluate the expression C C C C C C 5 In Exercises 20 and 21, tell whether the question can be answered using permutations or combinations. Explain your reasoning. Then answer the question. 20. Ninety-five tri-athletes are competing in a triathlon. In how many ways can 3 tri-athletes finish in first, second, and third place? 21. Your band director is choosing 6 seniors to represent your band at the Band Convention. There are 44 seniors in the band. In how many groupings can the band director choose 6 seniors? Copyright Big Ideas Learning, LLC Geometry 443

11 Name Date 12.6 Practice A In Exercises 1 and 2, make a table and draw a histogram showing the probability distribution for the random variable. 1. X = the letter that is spun on a wheel that contains 2 sections labeled A, five sections labeled B, and 1 section labeled C. 2. F = the type of fruit randomly chosen from a bowl that contains three apples, four pears, and four oranges. In Exercises 3 and 4, use the probability distribution to determine (a) the number that is most likely to be spun on a spinner, and (b) the probability of spinning an even number. 3. Probability P(x) Spinner Results Number on spinner x 4. Probability P(x) Spinner Results Number on spinner x In Exercises 5 7, calculate the probability of flipping a coin 20 times and getting the given number of heads Describe and correct the error in calculating the probability of rolling a five exactly four times in six rolls of a six-sided number cube. Copyright Big Ideas Learning, LLC Geometry 447

12 Name Date 12.6 Practice B In Exercises 1 and 2, make a table and draw a histogram showing the probability distribution for the random variable. 1. V = 1 if a randomly chosen letter consists only of line segments ( i.e. A, E, F, ) and 2 otherwise ( i.e. B, C, D, G, ). 2. X = the number of digits in a random perfect square from 1 to In Exercises 3 5, calculate the probability of flipping a coin 20 times and getting the given number of heads According to a survey, 22% of high school students watch at most five movies a month. You ask seven randomly chosen high school students whether they watch at most five movies a month. a. Draw a histogram of the binomial distribution for your survey. b. What is the most likely outcome of your survey? c. What is the probability that at most three people watch at most five movies a month. 7. Describe and correct the error in calculating the probability of rolling a four exactly five times in six rolls of a six-sided number cube ( ) 6C 1 5 4( ) ( ) Pk = 4 = A cereal company claims that there is a prize in one out of five boxes of cereal. a. You purchase 5 boxes of the cereal. You open four of the boxes and do not get a prize. Evaluate the validity of this statement: The first four boxes did not have a prize, so the next one will probably have a prize. b. What is the probability of opening four boxes without a prize and then a box with a prize? c. What is the probability of opening all five boxes and not getting a prize? d. What is the probability of opening all five boxes and getting five prizes? 448 Geometry Copyright Big Ideas Learning, LLC