Lesson 16.1 Assignment Name Date Rolling, Rolling, Rolling... Defining and Representing Probability 1. Rasheed is getting dressed in the dark. He reaches into his sock drawer to get a pair of socks. He knows that his sock drawer contains six pairs of socks, and each pair is a different color. Each pair of socks is folded together. The pairs of socks in the drawer are red, brown, green, white, black, and blue. a. How many possible outcomes are there in the experiment? b. What are the possible outcomes of the experiment? c. List the sample space for the experiment. d. Calculate the probability that Rasheed will choose a pair of blue socks, or P(blue). e. Calculate the probability that Rasheed will choose a pair of green socks, or P(green). f. Calculate the probability that Rasheed will choose a pair of socks that are not red, or P(not red). g. Calculate the probability that Rasheed will choose a pair of purple socks, or P(purple). Chapter 16 Assignments 293
Lesson 16.1 Assignment page 2 2. Consider the following bag containing seven marbles, each with a number written on it. An experiment consists of reaching into the bag and drawing a marble. 1 2 3 4 5 7 6 a. How many possible outcomes are there in the experiment? b. What are the possible outcomes of the experiment? c. List the sample space for the experiment. d. Calculate the probability of drawing the marble with the number 2 from the bag, or P(2). e. Calculate the probability of drawing a marble with an odd number from the bag, or P(odd). f. Calculate the probability of drawing a marble not containing the number 5 from the bag, or P(not 5). g. Calculate the probability of drawing a marble with the number 1, 2, 3, 4, 5, 6, or 7 from the bag, or P(1, 2, 3, 4, 5, 6, or 7). 294 Chapter 16 Assignments
Lesson 16.1 Assignment page 3 Name Date 3. Consider the square spinner shown and assume all sectors are the same size. An experiment consists of spinning the spinner one time. 17 3 q 11 a. How many possible outcomes are there in the experiment? b. What are the possible outcomes of the experiment? c. List the sample space for the experiment. d. Calculate the probability that the spinner stops on the sector with the letter q, or P(q). e. Calculate the probability that the spinner stops on a sector with a number, or P(number). f. Calculate the probability that the spinner stops on a sector with a number greater than 10, or P(number greater than 10). g. Calculate the probability that the spinner stops on a sector with a number less than 2, or P(number smaller than 2). Chapter 16 Assignments 295
Lesson 16.1 Assignment page 4 4. Determine whether each event is certain to occur, just as likely to occur as not to occur, or impossible to occur. Then write the probability. a. A coin is flipped and the coin lands heads up. Express the probability as a fraction. b. Tuesday follows Monday in the week. Express the probability as a percent. c. You have only white shirts in your closet. Express the probability of reaching into your closet and choosing a red shirt as a fraction. d. A box contains 2 green balls and 2 yellow balls. You reach into the box and grab a yellow ball. Express the probability as a decimal. 5. A box contains 2 black buttons, 2 white buttons, and 2 pink buttons. One button is drawn from the box at a time. a. List the sample space for the experiment. b. Calculate P(black). 296 Chapter 16 Assignments
Lesson 16.1 Assignment page 5 Name Date c. Calculate P(white). d. Calculate P(pink). e. What do you notice about all of the probabilities you calculated in parts (b) through (d)? g. Determine the sum of all of the probabilities from parts (b) through (d). 6. A box contains 4 black buttons, 4 white buttons, and 4 pink buttons. One button is drawn from the box at a time. a. Calculate P(black). b. Calculate P(white). c. Calculate P(pink). d. What do you notice about all of the probabilities you calculated in parts (a) through (c)? e. Determine the sum of all of the probabilities from parts (a) through (c). Chapter 16 Assignments 297
Lesson 16.1 Assignment page 6 7. A box contains 6 black buttons, 4 white buttons, and 2 pink buttons. One button is drawn from the box at a time. a. Calculate P(black). b. Calculate P(white). c. Calculate P(pink). d. Are the probabilities equal? Explain your reasoning. e. Determine the sum of all of the probabilities from parts (a) through (c). 298 Chapter 16 Assignments
Lesson 16.2 Assignment Name Date Toss the Cup Determining Experimental Probability 1. A tetrahedron is a four-sided solid, as shown. The faces of a tetrahedron are identical triangles. The number 1 is written on one face of the tetrahedron, the number 2 is written on a second face of the tetrahedron, the number 3 is written on a third face of the tetrahedron, and the number 4 is written on the fourth face of the tetrahedron. Suppose that you roll the tetrahedron 40 times. a. List the sample space. b. How many times do you expect the tetrahedron to show each of the four sides? c. Determine P(1), P(2), P(3), and P(4). Explain your calculations. Chapter 16 Assignments 299
Lesson 16.2 Assignment page 2 d. Suppose that you rolled the tetrahedron 40 times and recorded the results shown in the table. Complete the table by determining the totals and the experimental probabilities. Number Tally Total Experimental Probability 1 2 3 4 e. Compare the experimental probabilities you calculated in part (d) to the probabilities you calculated in part (c). Are they the same or different? Why? 300 Chapter 16 Assignments
Lesson 16.2 Assignment page 3 Name Date 2. Alfonso plays a game of bean bag toss by tossing a bean bag onto a large plastic mat with a large rectangle divided up into three smaller rectangles, as shown in the figure. A B C a. If Alfonso tosses the bean bag, in which rectangle does it have the best chance of landing? the least chance? b. Predict P(A), P(B), and P(C). c. Is there a way to determine the exact probabilities of landing on each of the rectangles? Explain your reasoning. Chapter 16 Assignments 301
Lesson 16.2 Assignment page 4 d. Alfonso plays the game by tossing the beanbag 40 times. His results are shown in the following table. Complete the table. Letter Tally Total Experimental Probability A B C e. If Alfonso plays the game again, do you think he will get the same results? Explain. f. Suppose the probabilities for the different rectangles are known to be: P(A) 5 1 P(B) 5 3 2 P(C) 5 1 10 5 If Alfonso tosses the bean bag 50 times, predict the number of times the bean bag would land on each rectangle. 302 Chapter 16 Assignments
Lesson 16.3 Assignment Name Date Double Your Fun Determining Theoretical Probability 1. Brett received the following dart board for his birthday. The rule book says that two darts are to be thrown and that individual s score is the sum of the two numbers. 4 2 6 8 a. List the sample space. b. Are all outcomes equally likely? Explain your reasoning. c. Complete the number array to determine all the possibilities for obtaining the sums. Dart 1 1 2 4 6 8 Dart 2 2 4 6 8 Chapter 16 Assignments 303
Lesson 16.3 Assignment page 2 d. How many possibilities are in the number array? e. Use the number array to help complete the tally table to determine the number of times each sum appears. Sum Tally 4 6 8 10 12 14 16 f. Calculate the theoretical probabilities for each sum. P(4) 5 P(10) 5 P(6) 5 P(12) 5 P(8) 5 P(14) 5 P(16) 5 304 Chapter 16 Assignments
Lesson 16.3 Assignment page 3 Name Date g. Calculate each probability. P(sum even) 5 P(sum greater than 8) 5 P(sum odd) 5 2 If two darts are thrown 80 times, how many times do you predict each of the following sums would occur? a. 8 b. 10 c. 14 Chapter 16 Assignments 305
Lesson 16.3 Assignment page 4 3. Determine if each probability can be determined experimentally, theoretically, or both. Explain your reasoning. a. Humans will land on Mars in the next 10 years. b. A number cube is rolled two times and the product of the two numbers is recorded. c. A box contains red, white, and blue marbles and you are not allowed to look inside the box. You reach in and grab a blue marble. d. A coin is tossed ten times and the results are recorded. e. The next car to pass you will be silver in color. 306 Chapter 16 Assignments
Lesson 16.4 Assignment Name Date A Toss of a Coin Simulating Experiments 1. Milton s dad likes to change the family computer s password every day. Milton is allowed to use the computer on Saturdays if he completes his homework and is able to choose the correct password. Every Saturday, Milton receives 3 sealed envelopes, each containing a password. Only one password is correct, and he is only allowed to choose one envelope. Suppose that this upcoming Saturday is the first of four Saturdays of this month. a. Estimate the number of times Milton will be able to use the computer this month by guessing. b. One model that you could use to simulate this problem situation is to choose 3 cards from a deck of cards. Suppose you choose the ace of spades (black), the ace of clubs (black), and the ace of diamonds (red). Shuffle the 3 cards and place them on a table face down. Draw a card. You win if you draw the ace of diamonds; otherwise you lose. What is the probability of drawing the ace of diamonds? c. Explain how the card method in part (b) simulates Milton s situation. d. Describe one trial of the experiment using the card method in part (b) if you want to simulate Milton s situation during the month. Chapter 16 Assignments 307
Lesson 16.4 Assignment page 2 e. Will one trial provide a good estimate of how many times Milton will get to use the family computer? Explain. f. Conduct 30 trials of the simulation using the card method described in part (b). Record your results in the table. Trial Number Number of Successes Trail Number Number of Successes 1 16 2 17 3 18 4 19 5 20 6 21 7 22 8 23 9 24 10 25 11 26 12 27 13 28 14 29 15 30 308 Chapter 16 Assignments
Lesson 16.4 Assignment page 3 Name Date g. Graph your results on the dot plot. 0 1 2 3 4 Number of Ace of Diamonds h. According to your simulation, about how many times should Milton expect to use the family computer during the month? 2. Describe a simulation to model each situation, and then describe one trial. a. When playing a certain video game, the rules require you to answer 5 true/false questions correctly simply by guessing. b. A box of yogurt-covered dried fruit contains equal amounts of 6 different kinds of dried fruit. You like only one of the 6 types and claim you can always pick what you like from the box correctly. To the unaided eye, however, all 6 different kinds of yogurt-covered dried fruit look alike. Chapter 16 Assignments 309
310 Chapter 16 Assignments
Lesson 16.5 Assignment Name Date Roll the Cubes Again Using Technology for Simulations 1. Milton is only allowed to use the family computer on Saturdays providing he knows the password to the system for that day. Each Saturday, Milton s dad gives him 3 new sealed envelopes containing one password each. Only one of the passwords is correct, and he is only allowed to choose one of the envelopes. Simulate how many times you expect Milton to be able to use the computer in one month that has four Saturdays. A simulation for Milton s situation can be designed using a computer spreadsheet. a. Describe one trial. b. Since there are 4 Saturdays in the month, use 4 columns in the first row of a spreadsheet to simulate one trial of choosing an envelope containing a password. Type the formula 5 RANDBETWEEN(1,3) in cell A1 and fill right to cell D1. Let the number 1 represent Milton choosing the password that works and the numbers 2 and 3 represent Milton choosing the passwords that do not work. List and interpret the results of your first trial. Chapter 16 Assignments 311
Lesson 16.5 Assignment page 2 c. Highlight the first row and then fill down through row 30. What does filling down through row 30 represent? d. Record your results in the table. Trial Number Number Correct Trial Number Number Correct 1 16 2 17 3 18 4 19 5 20 6 21 7 22 8 23 9 24 10 25 11 26 12 27 13 28 14 29 15 30 312 Chapter 16 Assignments
Lesson 16.5 Assignment page 3 Name Date e. Record your results on the dot plot. 0 1 2 3 4 Number of Correct Passwords Chosen f. What is the experimental probability of Milton using the family computer on Saturdays? Chapter 16 Assignments 313
Lesson 16.5 Assignment page 4 g. Is it likely that Milton will get to use the family computer on more than 2 Saturdays? Explain. h. If Milton runs more trials, is it likely that the experimental probabilities will be closer to the theoretical probabilities? Explain. 314 Chapter 16 Assignments