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1 Lesson.1 Skills Practice Name Date Left, Left, Left, Right, Left Compound Probability for Data Displayed in Two-Way Tables Vocabulary Write the term that best completes each statement. 1. A two-way table is a table that shows the relationship between two data sets, one organized in and one organized in. 2. A table is a table that shows how often each item, number, or event appears in a sample space. 3. A, also called a, shows the number of data points and their frequencies for two variables. 4. Data that can be grouped into categories, such as eye color and gender, are called or data. 5. A relative frequency is the ratio of occurrences within a category to the of occurrences. 6. A two-way relative frequency table displays the for two categories of data. Problem Set Of the students in Molly s homeroom, 11 students have brown hair, 7 have black hair, 5 have auburn hair, 4 have blonde hair, and 3 have red hair. Calculate each relative frequency. Round to the nearest thousandth if necessary. 1. brown hair 2. black hair auburn hair 4. blonde hair 5. red hair 6. brown or black hair 7. auburn or red hair 8. not brown hair Chapter Skills Practice 1171

2 Lesson.1 Skills Practice page 2 The two-way frequency table shows the number of students from each grade who plan to attend this year s homecoming football game. Grade Are you going to the homecoming game? Attending Homecoming Game Not Attending Homecoming Game Total Freshmen Sophomores Juniors Seniors Total Calculate the relative frequency of the entries in the two-way table. Round each relative frequency to the nearest tenth of a percent if necessary. 9. a freshman going to the homecoming game 31 < 17.8% a sophomore going to the homecoming game 11. a junior going to the homecoming game 12. a senior going to the homecoming game 13. a freshman not going to the homecoming game 14. a sophomore not going to the homecoming game 15. a junior not going to the homecoming game 16. a senior not going to the homecoming game 17. freshmen students 1172 Chapter Skills Practice

3 Lesson.1 Skills Practice page 3 Name Date 18. sophomore students 19. junior students. senior students 21. students from all grades going to the homecoming game 22. students from all grades not going to the homecoming game The two-way frequency table shows the current inventory of hardwood that a lumberyard carries. Suppose a board is selected at random from the lumberyard s inventory. Use the table to calculate each probability. Round to the nearest tenth of a percent if necessary. Size Type of Hardwood Oak Maple Cherry Total Total P(oak) 24. P(maple) % P(cherry) 26. P(1 3 2) 27. P(1 3 3) 28. P(1 3 4) Chapter Skills Practice 1173

4 Lesson.1 Skills Practice page P(1 3 6) 30. P(maple and 1 3 3) 31. P(oak and 1 3 2) 32. P(maple or cherry) 33. P(cherry or 1 3 4) 34. P(maple or 1 3 6) The two-way relative frequency table shows the results of a survey on the mayor s job approval. Suppose a member of the sample population is selected at random. Use the table of relative frequencies to calculate each probability. Express each probability as a decimal. Party Affiliation Do You Approve of the Mayor s Job Performance? Approve Disapprove No Opinion Total Republican Democrat Independent Total P(approve) 36. P(disapprove) P(no opinion) 38. P(republican) 39. P(democrat) 40. P(independent) 41. P(republican and disapprove) 42. P(democrat and no opinion) 43. P(independent and approve) 44. P(disapprove or no opinion) 1174 Chapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name Date 45. P(democrat or independent) 46. P(democrat or disapprove) 47. P(republican or approve) 48. P(independent or disapprove) Chapter Skills Practice 1175

6 1176 Chapter Skills Practice

7 Lesson.2 Skills Practice Name Date It All Depends Conditional Probability Vocabulary Define the term in your own words. 1. conditional probability Problem Set A five-sided letter die with faces labeled A, B, C, D, and E is rolled twice. The table shows the sample space of possible outcomes. Use the table to determine each probability. Express your answers as fractions in simplest form. Second Roll A B C D E A A, A A, B A, C A, D A, E First Roll B C B, A C, A B, B C, B B, C C, C B, D C, D B, E C, E D D, A D, B D, C D, D D, E E E, A E, B E, C E, D E, E 1. P(B on the first roll) 1 P(B on the first roll) 5 5 There are 25 possible outcomes and the 5 cells in row B represent getting a B on the first roll. So, P(B on the first roll) 5 15, or P(vowel on the second roll) Chapter Skills Practice 1177

8 Lesson.2 Skills Practice page 2 3. P(consonant on the second roll) 4. P(A or B on the first roll) 5. P(A on the first roll and consonant on the second roll) 6. P(vowel on the first roll and vowel or D on the second roll) 7. P(B or D on the second roll, given that the first roll was a consonant) 1178 Chapter Skills Practice

9 Lesson.2 Skills Practice page 3 Name Date 8. P(consonant on the second roll, given that the first roll was a vowel) 9. P(A on the second roll, given that the first roll was a vowel) 10. P(vowel on the second roll, given that the first roll was not an A) Determine each conditional probability. 11. Given P(A) , P(B) 5 0.3, and P(A and B) 5 0.1, determine P(B A). P(A and B) P(BuA) P(BuA) 5 P(A) Chapter Skills Practice 1179

10 Lesson.2 Skills Practice page Given P(A) 5 2, P(B) 5 3 9, and P(A and B) , determine P(A B) Given P(A) 5 5, P(B) 5 1, and P(A and B) , determine P(B A) Given P(A) , P(B) 5 0.2, and P(A and B) , determine P(A B) Chapter Skills Practice

11 Lesson.2 Skills Practice page 5 Name Date The jar on Mrs. Wilson s desk contains green paper clips, 30 red paper clips, 15 white paper clips, and 10 black paper clips. She selects a paper clip without looking, does not replace it, and selects another. Determine each probability. Round each answer to the nearest tenth of a percent if necessary. 15. P(both paper clips are red) The probability of choosing two red paper clips is approximately 15.7%. P(red 1st and red 2nd) 5 P(red 1st)? P(red 2nd) 5 30? ? < P(both paper clips are white) 17. P(second paper clip is green first paper clip is black) Chapter Skills Practice 1181

12 Lesson.2 Skills Practice page P(second paper clip is white first paper clip is red) 19. P(second paper clip is green first paper clip is not green). P(second paper clip is not red first paper clip is red) 1182 Chapter Skills Practice

13 Lesson.2 Skills Practice page 7 Name Date The two-way frequency table shows the results of a study in which a new topical medicine cream was tested for its effectiveness in treating poison ivy. Half of the study participants applied the cream to their poison ivy for 3 days and noted any changes in their symptoms. The other half applied a placebo and noted any changes. Results Treatment Medicine Cream Placebo Significant improvement 21 9 Moderate Improvement No Improvement 4 12 Total Total Use the table to determine each probability. Round each answer to the nearest tenth of a percent if necessary. a. P(significant improvement medicine cream) P(significant improvement u medicine cream) 5 60% P(medicine cream and significant improvement) P(significant improvement given medicine cream) 5 P(medicine cream) b. Are significant improvement and medicine cream treatment independent or dependent events? Explain your reasoning. Significant improvement, S, and medicine cream treatment, M, are dependent events because the value of P(S u T) is not equal to the value of P(S). P(S u M) P(S) Chapter Skills Practice 1183

14 Lesson.2 Skills Practice page Use the table to determine each probability. Round each answer to the nearest tenth of a percent if necessary. a. P(placebo no improvement) b. Are no improvement and placebo treatment independent or dependent events? Explain your reasoning Chapter Skills Practice

15 Lesson.2 Skills Practice page 9 Name Date 23. Use the table to determine each probability. Round each answer to the nearest tenth of a percent if necessary. a. P(medicine cream moderate improvement) b. Are medicine cream treatment and moderate improvement independent or dependent events? Explain your reasoning. Chapter Skills Practice 1185

16 Lesson.2 Skills Practice page Use the table to determine each probability. Round each answer to the nearest tenth of a percent if necessary. a. P(placebo significant improvement) b. Are placebo treatment and significant improvement independent or dependent events? Explain your reasoning Chapter Skills Practice

17 Lesson.3 Skills Practice Name Date Counting Permutations and Combinations Vocabulary Define each term in your own words. 1. factorial 2. permutation 3. combination 4. circular permutation Problem Set Evaluate each expression P 3 P 5 8! 5 8! (8 2 3)! 5! 2. 5 P 5 Chapter Skills Practice 1187

18 Lesson.3 Skills Practice page P P P P 6 Calculate the number of possible outcomes in each of the following situations. 7. A computer code uses 4 randomly selected letters of the alphabet. If no letters are repeated, how many possible codes are there? There are 358,800 possible codes. 26 P , Twelve students are competing in the finals of a spelling bee. The top 3 finishers are awarded a gold, silver, and bronze medal. In how many ways can the medals be won? 9. A summer camp offers 12 different afternoon activities. Caleb selects 2 of the activities to do today. How many possible outcomes are there if the order of the activities is important? 10. There are 15 different seminars at a teacher s convention. Mrs. Alvarez will choose 3 of the seminars to attend today. How many possible outcomes are there if the order of the seminars is important? 1188 Chapter Skills Practice

19 Lesson.3 Skills Practice page 3 Name Date Evaluate each expression C C 5 C 5 11! 11 4 (11 2 4)!4! = 11! !4! C C C C 2 Calculate the number of possible outcomes in each of the following situations. 17. A committee of 4 students is to be formed from a homeroom of 25 students. How many different committees are possible? C 5 25! 5 12, !4! 18. A pizzeria offers 8 different toppings on their pizzas. If a customer wants to order a 3-topping pizza, how many possible options are there? 19. Seven friends are playing musical chairs. In the first round there are 5 chairs, so only 5 of the friends will move on to the second round. How many different groups of friends are possible for the second round of the game?. Fran has 4 pennies, 3 nickels, 5 dimes, and 2 quarters in her pocket. In how many ways can she pull 3 coins out of her pocket if the order of the coins is not important? Chapter Skills Practice 1189

20 Lesson.3 Skills Practice page 4 A website requires users to enter a 6-digit personal identification number (PIN) for security. A user s PIN must use the digits 1, 2, 3, 4, 5, and 6, and no digit can be used more than once. Determine each probability. Express your answers as fractions in simplest form. 21. Suppose a user is unable to remember his PIN and enters the digits randomly. What is the probability that he will guess correctly? The probability of guessing correctly is 1 7. There is 1 correct PIN and I determined the total possible number of PINs by calculating 6 P 6, which equals 7. So, the probability of guessing correctly is Suppose a user randomly selects a PIN. What is the probability that the user s PIN is an even number? 23. Suppose a user randomly selects a PIN. What is the probability that the user s PIN begins with 3 even digits and ends with 3 odd digits? 1190 Chapter Skills Practice

21 Lesson.3 Skills Practice page 5 Name Date 24. Suppose a user randomly selects a PIN. What is the probability that the user s PIN begins with the digits 123? A group of 6 seniors, 5 juniors, and 4 sophomores are running for student council. The council is made up of 6 members. Assume that each student has an equal chance of being elected to student council. Determine each probability and express your answers as fractions in simplest form. 25. What is the probability that 2 seniors, 2 juniors, and 2 sophomores are elected? The probability of choosing 2 seniors, 2 juniors, and 2 sophomores is There are 15 ways to choose 2 seniors: 6 C There are 10 ways to choose 2 juniors: 5 C There are 6 ways to choose 2 sophomores: 4 C So, there are 900 ways to choose 2 seniors, 2 juniors, and 2 sophomores: There are 5005 ways to choose 6 student council members from a pool of 15 candidates: C So, the probability of choosing 2 seniors, 2 juniors, and 2 sophomores is 900, or What is the probability that the student council is made up of all seniors? Chapter Skills Practice 1191

22 Lesson.3 Skills Practice page What is the probability that 3 seniors, 2 juniors, and 1 sophomore are elected? 28. What is the probability that 3 juniors and 3 sophomores are elected? Calculate the number of ways the letters of each word can be arranged. 29. SUNNY 30. FACTORIAL The letters in the word SUNNY can be arranged 60 different ways. 5! ! 31. ARRANGE 32. PROBABILITY 33. PARALLEL 34. MISSISSIPPI 1192 Chapter Skills Practice

23 Lesson.3 Skills Practice page 7 Name Date Calculate the number of ways each arrangement can be made flowers planted around the base of a tree The flowers can be arranged around the base of the tree in 39,916,800 different ways. (12 2 1)! 5 11! 5 39,916, dinner guests seated around a table candles arranged around the outside of a circulate birthday cake baseball players standing in a circle under a fly ball teachers seated around a circular table at a conference kittens arranged around a ball of yarn Chapter Skills Practice 1193

24 1194 Chapter Skills Practice

25 Lesson.4 Skills Practice Name Date Trials Independent Trials Problem Set Determine the probability in each situation. Express your answers as fractions in simplest form. 1. On average, Malcolm makes a par on 2 of the golf holes that he plays. What is the probability that he 3 will make a par on each of the next 2 holes that he plays? 4 The probability that Malcolm makes a par on the next 2 holes is 9. Let PAR represent making par on one hole. P(PAR 1st and PAR 2nd) 5 2 P(PAR 1st )? P(PAR 2nd ) 5 4? Clarence rolls 2 number cubes. What is the probability that he will roll a number greater than 4 on both rolls? 3. For every 5 penalty kicks that Missy attempts, she scores on average 3 goals. What is the probability that Missy will score 2 goals in her next 2 penalty kick attempts? Chapter Skills Practice 1195

26 Lesson.4 Skills Practice page 2 4. On average 3 out of 4 students order spaghetti at the cafeteria when it is offered. What is the probability that the first 2 students in line for lunch will have spaghetti if it is offered? 5. A spinner has 8 equal size spaces with the colors: red, green, yellow, red, blue, white, green, red. If the spinner is spun twice, what is the probability of spinning red on both spins? 6. The table shows the results of a survey of likely voters. Suppose 2 likely voters are selected at random. Based on the results of the survey, what is the probability that both likely voters support Issue #1? Do You Support Issue #1? Response Strongly Oppose Somewhat Oppose No Opinion Somewhat Support Strongly Support Frequency Chapter Skills Practice

27 Lesson.4 Skills Practice page 3 Name Date According to a recent survey, 80% of high school students have their own cell phone. Suppose 10 high school students are selected at random. Determine each probability. Round your answers to the nearest tenth of a percent if necessary. 7. P(8 of the students have cell phones) C 10 8 (0. 8) 8 (0. 2) % 8. P(5 of the students have cell phones) 9. P(3 of the students do not have cell phones) 10. P(all of the students have cell phones) 11. P(9 of the students have cell phones) 12. P(none of the student shave cell phones) Based on past results, a batter knows that the opposing pitcher throws a fastball 75% of the time and a curveball 25% of the time. Suppose the batter sees 8 pitches during a particular at-bat. Determine each probability. Round your answers to the nearest tenth of a percent if necessary. 13. P(4 fastballs and 4 curveballs) C 8 4 (0. 75) 4 (0. 25) % 14. P(all fastballs) 15. P(5 fastballs and 3 curveballs) Chapter Skills Practice 1197

28 Lesson.4 Skills Practice page P(5 curveballs and 3 fastballs) 17. P(7 fastballs and 1 curveball) 18. P(no fastballs) 1198 Chapter Skills Practice

29 Lesson.5 Skills Practice Name Date To Spin or Not to Spin Expected Value Vocabulary Write the term that best completes each statement. 1. Geometric probability is a of measures such as length, area, and volume. 2. The expected value is the value when the number of trials is large. Problem Set Determine the probability that a dart that lands on a random part of each target will land in the shaded scoring section. Assume that all squares in a figure and all circles in a figure are congruent unless otherwise marked. Round each answer to the nearest tenth of a percent if necessary in. 16 in. 10 in. 16 in. The probability of a dart landing in the shaded area is approximately 78.5%. Area of Entire Board: 10(10) in. 2 Area of Shaded Section: 5 2 p i n. 2 Probability of Landing in Shaded Section: % 100 Chapter Skills Practice 1199

30 Lesson.5 Skills Practice page in. 15 in. in in in. 15 in. 16 in. 5 in. 15 in. in. 5 in. 10 Chapter Skills Practice

31 Lesson.5 Skills Practice page 3 Name Date 7. in in. 18 in. 10 in. 6 in. 6 in. Benjamin rolls a six-sided number cube 12 times. Determine each expected value and explain your solution method. 9. How many of the outcomes do you expect to result in a 1? I would expect 2 out of the 12 outcomes to result in a (12) How many of the outcomes do you expect to result in a 1 or a 6? 11. How many of the outcomes do you expect to result in number greater than 2? Chapter Skills Practice 11

32 Lesson.5 Skills Practice page How many of the outcomes do you expect to result in an even number? Calculate the expected value of spinning each spinner one time. Round to the nearest hundredth if necessary ( 1 3 ) 1 6 ( 1 3 ) 1 8 ( 1 3 ) Chapter Skills Practice

T894 Mathematics Success Grade 7 [OBJECTIVE] The student will find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. [PREREQUISITE SKILLS] Simple probability,

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