Data Analysis and Probability

Transcription

1 CHAPTER 1 Data Analysis and Probability Solutions Key ARe you ready? 1. D. B. F. E. A. x 1 x x 9 x x. 1 x 1 1x 7 1x 1 1 x x x 1. x 9. 1 x 1 1. > 1, 1x, 1 1x 1 1 x 11. > 1 1. < , 1,,, ,., 1,, , % 9. %. % 1. 1% 1-1 organizing and displaying data Check it out! 1a. bread b. cheese and mayonnaise. 1,, and ; about 1, people. The difference in temperature is about, - 1 F. Prices increased from January through July or August, and then prices decreased through Nov.. There is a total of c Therefore the percentage of cantaloupe in the fruit 1 salad is 1.%. A circle graph is appropriate for this data because it shows categories as parts of a whole. Sleeping:.7 7.% 1 Eating:.7.7% 1 School:. % 1 Sports: 1..% 1 Homework: 1..% 1 Other: % 1 Find the angle measure for each sector of the graph. Since there are in a circle, multiply each percent by. Sleeping:.7 1 Eating:.7 School:. 9 Sports:. Homework:. Other:.1 1 Use a compass to draw a circle. Mark the center and use a straightedge to draw one radius. Then use a protractor to draw each central angle. Homework, 1 Sports, 1 Think and discuss Vera s Day Other, 17 School, Sleeping, Eating, 1. Possible answer: You can compare quantities.. Possible answer: The horizontal and vertical scales start at, time is placed on the horizontal axis, and even intervals are used between items on the horizontal axis.. Graph Compare categories Bar Graph Show change over time Line Graph Show how a whole is divided into parts Circle Graph 1 Holt McDougal Algebra 1

2 Exercises Guided practice 1. one part of a whole. As the steepness of the line increases, the rate of change increases.. animals. cats; rabbits. club level seat is about $1 more expensive in stadium A than at stadium B. box seats 7. Prices at stadium A are greater than prices at stadium B.. about, tickets 9. between weeks and 1. 1 week before election 11. The difference in support weeks before election was about 1%. 1. Support for candidate A generally decreased, and support for candidate B generally increased. 1. purple 1. Yellow balls are, % of 1 1. Blue and green are approximately equally represented. 1. A circle graph is appropriate for this data because it shows categories as parts of a whole. Clothing:. % 1 Food:. % 1 Entertainment:. % 1 Other: 1.1 1% 1 Find the angle measure for each sector of the graph. Since there are in a circle, multiply each percent by. Clothing:. 1 Food:. 9 Entertainment:. 9 Other:.1 Use a compass to draw a circle. Mark the center and use a straightedge to draw one radius. Then use a protractor to draw each central angle. Entertainment, $ Karim s Budget Other, $1 Practice and problem solving Clothing, $ Food, $ 17. Difference between the tribes with largest and smallest population is about,. 1. Total population is about,. Therefore percentage of Cherokee is 1,, % 19. Fri. Wed 1. There are about 1 dinner customers and lunch customers. Therefore there are about. times as many dinner customers on Sunday.. games 1 and. games, and. Value for stock X is $, and value for stock Y is $. So the average value for both stocks is $... Stock Y changed the most between Apr. and Jul. of.. Both generally increased. 7. There is a total of 9 cars. So, there is 9 1 % hopper cars.. Percentage of gondola or tank cars is, ( + 11) 9 9 % 9. A double-line graph is appropriate since it shows change over time for two things. It also allows you to compare two things. Determine the scale and interval for each data set of data. Time should be plotted on the horizontal axis because it is independent. Plot a point for each pair of values. Connect the points using line segments. Title the graph and label the horizontal and vertical scales. Weights of Twin Babies Weight (lb.) Boys 1 1 Age (d) Girls. line 1. double line. bar. circle. Possible answer: line graph: your height over time; circle graph: your CD collection divided into categories; double-bar graph: number of hours you spend on homework or sports each day of the week a. Greece; about % b. United States; about 1%. If the graph is generally increasing, you can predict that the value in the future will increase. Holt McDougal Algebra 1

3 test prep 7. D. G 9. A bar graph allows you to compare categories. Determine an appropriate scale and interval. The scale must include all of the data values. The scale is separated into equal parts, called intervals. Use the data to determine the lengths of the bars. Draw bars of equal width. Title the graph and label the horizontal and vertical scales. Algebra 1 Classrooms Students 1 challenge and extend. museum Mr. Abrams Ms. Belle Mr. Marvin Ms. Swanson Teacher 1. About % of people who went to the museum were girls. So, % of. 19 girls. The graph shows only the percentages of each group made up of teachers, boys and girls. It does not tell how many people went to each trip. 1- and histograms check it out! 1. Stem Leaves Key: 1 9 means 19. Identify the least and greatest values. The least value is. The greatest value is 1. Divide the data into equal intervals. For this data set, use intervals of. List the intervals in the first column of the table. Count the number of data values in each interval and list the count in the last column. Interval Use the scale and interval from the frequency table. Draw a bar for the number of vacations in each interval. Vacation Number Length a. Choose intervals for the first column of the table. Record the frequency of values in each interval for the second column. Add the frequency of each interval to the frequencies of all the intervals before it. Put that number in the third column of the table. b. 9 Interval Cumulative think and discuss 1. leaves. The stems are the intervals, and the number of leaves for each stem gives the height of the bar.. How are they alike? Both use bars and categories. Both make it easy to compare categories. Exercises Guided Practice 1. stem-and-leaf plot. Stem Leaves Bar Graphs vs. Histograms Key: 1 means 1. Austin Stem New York Key: 1 means.1 How are they different? In a histogram, the bars touch. A histogram shows consecutive intervals. Holt McDougal Algebra 1

4 . Identify the least and greatest values. The least value is 19. The greatest value is. Divide the data into equal intervals. For this data set, use intervals of. List the intervals in the first column of the table. Count the number of data values in each interval and list the count in the last column. Interval Use the scale and interval from the frequency table. Draw a bar for the number of breaths in each interval. 1 Breathing Intervals Length (min.) a. Choose intervals for the first column of the table. Record the frequency of values in each interval for the second column. Add the frequency of each interval to the frequencies of all the intervals before it. Put that number in the third column of the table. b. Interval Cumulative Practice and problem solving 7. Summer Stem Winter Key: 1 1 means 11, 7 means 7. Stem Leaves Key: means 9. The least value is.. The greatest value is.9. For this data set, use intervals of.. Interval Use the scale and interval from the frequency table. Draw a bar for the number of elements in each interval. Nonmetal Elements Atomic Mass a. The least value is. The greatest value is 7. For this data set, use intervals of. b. 1 Interval Cumulative City Mileage Stem Highway Mileage Key: means means 1a. Stem Leaves Key: 9 means 9 Holt McDougal Algebra 1

5 b. Use the scale and interval from the frequency table. Draw a bar for the number of grades in each interval. Intervals of Number Grade c. Use the scale and interval from the frequency table. Draw a bar for the number of grades in each interval. Intervals of 1 1a. The least value is 1. The greatest value is 1. For this data set, begin at 1 and use intervals of 1. Interval b. Use the scale and interval from the frequency table. Draw a bar for the number of weights in each interval. Weightlifting Number Number Grade 1d. Use the scale and interval from the frequency table. Draw a bar for the number of grades in each interval. Intervals of Number Grade 7 9 1e. As the size of the intervals increases, the number of bars decreases. 1f. The histogram that uses intervals of ; It makes Damien s grades look higher because the bar for 7 9 is much taller than the bar for A; there is no stem for Weight (kg) c. No; she did not lift one of the three greatest weights. 1. Use the scale and interval from the frequency table. Draw a bar for the number of movies in each interval. Top Ten Movie Sales Number Gross (million $) 17. The intervals are not the same size, so the histogram may not accurately represent ages under 1 or over. test prep 1. B 19. G. D challenge and extend 1. Interval Cumulative Holt McDougal Algebra 1

6 1- DATA DISTRIBUTIONS CHECK IT OUT! 1. 1, 1, 1, 1, lb median: 1, 1, 1, 1, 1 The median is 1 lb. mode: 1 lb and 1 lb range: 1-1 lb. 1,,, 7,, Write the data in numerical order., 1,,, 7, The outlier is. With the Outlier: ( ) 1. median:, 1,,, 7, The median is. mode: range: - 7 Without the Outlier: ( ). median: 1,,, 7, The median is. mode: range: The outlier decreases the mean by.7 and increases the range by 1. It has no effect on the median and mode.. a. mode: 7 b. Find the mean and median ,, The median is 1. median: 7, 7, Josh should use the median, 1, since it is greater than either the mean or the mode.. 1, 1, 1, 1, 1, 17, 1, 1, 1, 19, 11, 1, 1, 1,, Order the data from least to greatest. 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 19,, Identify the five needed values. minimum: 11 first quartile: 1 maximum: third quartile: 1 median: a. The data set for ; the distance between the points for the least and greatest values is less for than for 7. b. Find the medians and subtract. 7 median: about $1 million median: about $1 million 1-1 The median ticket sales were about $ million more. THINK AND DISCUSS 1. Either the data set has an odd number of values, or the data set has an even number of values and the two middle values are the same.. Possible answer: 1,, 9; start with two numbers and a variable, where the variable is the greatest number in the set: 1,, x. The median of this set is, so the mean must be. Write an equation for the x. Solve for x. Multiply both sides by : x 1. Solving yields x 9.. Because the minimum and the first quartile are the same, the box-and-whisker plot would have no whisker on the left side.. Measures of Central Tendency Measure mean median mode Use to Answer What is the average? What is the halfway point of the data? What is the most common value? EXERCISES GUIDED PRACTICE 1. The range is the difference between the greatest and least values. The interquartile range is the difference between the third and first quartiles..,,, median:,,, The median is. mode: range: -. 1,,,,, median: 1,,,,, The median is.. mode: range: ,,, 1,,,, median: 1, 1,,,,,, The median is 1. mode: 1,, and range: , 7, 7, 7, 7,,, median: 71, 7, 7, 7, 7,,, The median is 7. mode: 7 range: Holt McDougal Algebra 1

7 . 1, 9, 1, 17, 1 Write the data in numerical order. 1, 1, 1, 17, 9 The outlier is 9. With the Outlier: Without the Outlier: median: 1, 1, 1, 17, 9 The median is 1. mode: no mode range: median: 1, 1, 1, 17 The median is 1.. mode: no mode range: The outlier increases the mean by 1., increases the median by 1., and increases the range by 79. It has no effect on the mode. 7., 7, 7, 1, Write the data in numerical order. 1,,, 7, 7 The outlier is 1. With the Outlier: median: 1,,, 7, 7 The median is. mode: range: 7-1 Without the Outlier: median:,, 7, 7 The median is. mode: range: 7-11 The outlier decreases the mean by 11.1, decreases the median by, and increases the range by 1. It has no effect on the mode.. Find the mean, median, and mode median:,,,, 91 The median is. mode: no mode median: ; the mean is lower than all but one of the scores because of the outlier. There is no mode. 9. median: ; the median is greater than the mean, and there is no mode. 1. 1, 1,,,, Order the data from least to greatest. 1,,,,, 1 Identify the five needed values. minimum: 1 first quartile: maximum: 1 third quartile: median: , 1,,,, Identify the five needed values. minimum: 1 first quartile: 1 maximum: third quartile: median: Simon; the vertical line in the box for Simon is farther to the right than the vertical line in the box for Natasha. 1. Simon; the left point is farther to the left at about points. PRACTICE AND PROBLEM SOLVING 1. 7,, 9, median:, 7, 9, 91 The median is. mode: no mode range: ,,,,,,, median: 1,,,,,,, The median is.. mode: and range: ,, 1, 19,,, 1, median: 19, 19,,, 1, 1,, The median is. mode: 19, 1, and range: ,,,,, 1, median:,,,,, 1, The median is. mode: range: Holt McDougal Algebra 1

8 1.,,, 7, 9 Write the data in numerical order., 9, 7,, The outlier is. With the Outlier: median:, 9, 7,, The median is 7. mode: no mode range: - Without the Outlier: median: 9, 7,, The median is 9.. mode: no mode range: - 9 The outlier decreases the mean by., decreases the median by., and increases the range by 1. It has no effect on the mode. 19.,,,,, Write the data in numerical order.,,,,, The outlier is. With the Outlier: median:,,,,, The median is.. mode: range: - Without the Outlier: median:,,,, The median is. mode: range: - The outlier increases the mean by, increases the median by., and increases the range by 1. It has no effect on the mode.. Find the mean, median, and mode median: 1, 1, 1, 1 The median is 1.. mode: no mode The mean, 1, gives Lamont s average score. 1. 1; the mean is greater than the median and there is no mode..,,,,,, Order the data from least to greatest.,,,,,, Identify the five needed values. minimum: first quartile: maximum: third quartile: median:., 9, 1, 1, 9, Order the data from least to greatest. 1,,, 9, 9, 1 Identify the five needed values. minimum: 1 first quartile: maximum: 1 third quartile: 9 median: Sneaks R Us, about $1. Sneaks R Us; the middle half of the data doesn t vary as much at Sneaks R Us as at Jump N Run.. about $ 7. 1,,,,,, 7,, 9, median: 1,,,,,, 7,, 9, 1 The median is.. mode: none range: ,,,, median:,,,, The median is. mode: range: ,.1,.,., median: 1.,.1,.,.,. The median is.. mode: none range: , 1, 1,, median:, 1, 1,, 1 The median is 1. mode: none range: ,,,, median:,,,, The median is. mode:, range: - 1. Holt McDougal Algebra 1

9 . -, -, -, -, -, -1 (-) + (-) + (-) + (-) + (-) + (-1) -1-1 median: -, -, -, -, -, -1 The median is - 1. mode: - range: (-1) - (-). 1,, 9, 1,, median: 1,, 9, 1,, The median is 1 1. mode: none range: ,, 1, 1, 1, median:,, 1, 1, 1, The median is 1. mode: 1 range: -. Possible answer: 17 Possible answer: 17. sometimes 7. sometimes. always 9. always. never 1. Median; the mean is affected by the outlier of 11, and there is no mode.., 71, 7, 7, 7, 71, 7, 71, 7, 7, 79 Without 7 F: F median:, 71, 71, 71, 7, 7, 7, 7, 7, 7, 79 The median is 7 F. mode: 71 F range: F With 7 F: ( ) F median:, 7, 71, 71, 71, 7, 7, 7, 7, 7, 7, 79 The median is 7. F. mode: 71 range: The mean would decrease by. F, the median would decrease by. F, and the mode and range would not change.. Find the mean, median, and mode $. median:,,,, 1 The median is $.. mode: $. The home-decorating store should advertise the median or mode. The store wants their prices to appear low, and the median and the mode are both $. less than the mean..,,, 1, 1, 1,,,, 1 Order the data from least to greatest. 1, 1, 1, 1,,,,,, Identify the five needed values. minimum: 1 first quartile: 1 maximum: third quartile: median: ,,, 7, 11, 1, 17, 19,, 9, 1 Identify the five needed values. minimum: first quartile: maximum: 1 third quartile: median: , 1, 1, 1,,,,,,,,,, Identify the five needed values. minimum: 1 first quartile: 1 maximum: third quartile: median: ,,,,,,,,, Order the data from least to greatest.,,,,,,,,, Identify the five needed values. minimum: first quartile: maximum: third quartile: median: 9 Holt McDougal Algebra 1

10 . a..9,.,.7,.7,.7,.7,.,.,.,.,. ( ) 11. median:.,.,.,.,.,.7,.7,.7,.7,.,.9 The median is.7. mode:.7 range: b..9 m 9. Write the numbers from the stem-and-leaf plot. Then find the mean and median.,,,,,,, $, median:,,,,,,, 7 The median is $,. The median describes the typical salary of an employee at this company better because the outlier of $7, increases the mean significantly.. a. 1,,,,, 1, 1, b. The mean increases by c. 1.7 The mean is multiplied by. 1. Let t represent the score Allison needs on her next test to have a mean of 9% t 9 + t 9 () + t 9() + t - - t 9 Allison needs a test score of 9 on her next test to have a mean of 9%..,, 1,,,, 7, Possible answer: No, Earth s number of moons is much less than either the mean or median number moons per planet.. An outlier with a large value will increase the mean, and an outlier with a small value will decrease the mean. TEST PREP. B. G mean lengths of alligators: mean lengths of crocodiles: C mean with Rex s weight: mean without Rex s weight:. The mean decreases by. pounds. CHALLENGE AND EXTEND. Possible answer:,, 7, 9, 1 9. Check students work.. a. mean of homework scores: mean of test scores: 7 b. weighted average: (.) + 7(.) + 9(.) c. mean score without weighted 1- average: ( ) 1.1 misleading graphs and statistics check it out! 1. Possible answer: company D; because the fertilizer from company D appears to be more effective than the other fertilizers.. Possible answer: taxi drivers; the drivers could justify charging higher rates by using this graph, which seems to show that gas prices have increased dramatically.. Possible answer: Smith; Smith might want to show that he or she got many more votes than Atkins or Napier.. The sample size is much too small to make a conclusion for a large population. think and discuss 1. Possible answer: someone selling a product might want to make it seem much better than other products. Holt McDougal Algebra 1

11 . Exercises The scale might not start at. A sample might not be large enough. guided practice Ways that Graphs and Statistics can be Misleading The sectors of a circle graph might not add to 1%. A sample might not be random. 1. Random sample means that no member of a group is more likely to be picked for the sample than any other member of the group. a. The vertical scale does not start at. This exaggerates the difference in heights of the bars. b. Employees at company Y make about twice as much as employees at company Z. c. Possible answer: company Y might want to use the graph to show how well its employees are paid; the graph makes it appear that company Y pays high salaries. a. The vertical scale does not start at, and the categories on the horizontal scale are not at equal time intervals. b. Tourism is decreasing rapidly. c. Possible answer: someone who wants to increase spending on promoting tourism in San Francisco; the graph makes it appear that San Francisco is becoming a less popular travel destination. a. The sectors of the graph do not add up to 1%. b. Because of the graph someone may believe that the granola bar is almost half protein. c. Possible answer: the granola bar company might want to use this graph to make their product look healthful.. The sample size is too small to make conclusions for a large population.. People shopping at the mall are more likely to favor a larger parking lot, while they may not be from the community next to the mall. practice and problem solving 7a. The vertical scale does not start at. b. Single men pay significantly more than single women. 7c. Possible answer: single men looking for apartments who want to negotiate a lower rent might want to use this graph; the graph makes it appear that single men are overcharged. a. The vertical scale does not start at, and it uses larger values beyond the needed ones. b. Someone might believe that the price has not changed very much at all. c. Possible answer: coffee growers; the graph makes it appear that coffee prices are low. 9a. The sectors of the graph do not add up to 1%. b. Someone might believe that almost half of the state s spending was for welfare. 9c. Possible answer: Someone who wants to justify cutting spending on welfare; the graph makes it appear that a large part of the spending was for welfare. 1. Most of the classes have fewer than students. The mean is not a good descriptor because there is an outlier. 11a. Average score: c. b. The lowest score,., brings the mean lower than most of the scores. Score 1 Women s Gymnastics Scores 1 7 Rank 1. B; the vertical scale extends beyond what is needed, so it appears that the population grew slowly; however, the population is several times the size that it started. 1a. Internet Service Connection Speed (kbps) Speedy Online 91 Provider TelQuick Alacrity b. Internet Service Connection Speed (kbps) Speedy Online TelQuick Alacrity Provider 1 Holt McDougal Algebra 1

12 1c. Possible answer: an objective report or Alacrity materials. Someone who has no reason to make one company look better than another might make this graph. Alacrity might make this graph to show that they are very similar to the other companies. 1. Possible answer: The scale of a graph can exaggerate the differences in the heights of bars or the slopes of lines. The data may be accurate, but the display encourages an inaccurate interpretation. test prep 1. B 1. H challenge and extend 17a. The first question asks whether two people have the same fingerprint. The second question asks whether someone could have made a mistake. b. The fingerprint had to belong to Dr. Arenson. 17c. Someone who wants to prove that the fingerprint belongs to Dr. Arenson. 17d. The fingerprint might not belong to Dr. Arenson. 17e. Someone who wants to prove that the fingerprint does not belong to Dr. Arenson. 1a. Most deaths during the Crimean War were due to unclean conditions. b. Possible answer: military officials who could control the conditions of military hospitals. ready to go on? Section A Quiz 1. Paper/cardboard: 11. % Therefore, paper/cardboard represents over % of Don s recyclables.. Don recycles: lb. Glass:. %. A line graph shows change over time. Proceeds (thousands of $). Stem Leaves Key 7 means $7, Fundraiser 7 Time (PM) a. The least value is 1. The greatest value is. For this data set, use intervals of. Interval b. Party Attendance 7a. 1.7 median:,,,, 7,, 1,, 9 The median is 9. mode: 1 b. mean People 9, 9, 1, 1, 1, 7c. Median or mode; the mean is lower than most of the temperatures because one day had a high of only F.. minimum: ; first quartile: maximum: 9; third quartile: The vertical axis begins at. This might make someone believe that the value of the stock has decreased dramatically. Another company might want to devalue this company s stock. 1. The survey did not address a random sample. Because the survey was online, those who responded were probably already somewhat comfortable using technology. 1- experimental probability check it out! 1. sample space: {1,,,,, } outcome shown:. A standard number cube is numbered 1 through. This event is certain. 7 a b a % The experimental probability that a toothbrush does not have a defective motor is 99.%. b. Find 99.% of,. (.99)(,),9 There are,9 motors that are likely to have no defects. Holt McDougal Algebra 1

13 think and discuss 1. Possible answer: An outcome is one possible result of an experiment. An event is a set of outcomes.. No; different outcomes may occur with different frequencies each time the experiment is carried out. The more trials performed, the more accurate the estimate is likely to be.. Impossible: Rolling a 7 on a number cube exercises guided practice Unlikely: Rolling a 1 on a number cube Likelihood of an Event As Likely as Not: Rolling a 1,, or on a number cube Likely: Rolling a number less than on a number cube 1. picking a shoe at random from a pair of shoes. sample space: {1,,,,, } outcome shown:. sample space: {blue, red, yellow, green} outcome shown: red Certain: Rolling a number less than 7 on a number cube. sample space: {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} outcome shown: THT. Peter and Thomas were born in different months. This event is impossible.. The team won 9 of 1 games. The team is likely to win the next game. 7. Getting a number out of possible numbers. This event is unlikely.. number of times event occurs number of times event occurs a. number of times event occurs 1 % The experimental probability that Elyse will roll a strike on any frame is %. b. A game consists of 1 frames. Find % of 1 frames. (.)(1) Elyse is likely to throw strikes in 1 games. practice and problem solving 1. sample space: {HH, HT, TH, TT} outcome shown: TT 1. sample space: {blue, red, yellow} outcome shown: blue 1. sample space: {blue, yellow, green, red} outcome shown: green 1. Marlo takes one out of two shoes from the box. This event is as likely as not. 1. The bus has been late two out of ten days. This event is unlikely. 17. There can be either one or two quarters landing on heads. This event is likely a. % The experimental probability that a ski chosen at random will be defective is %. b. Find % of. (.)() 1 There are 1 skis that are likely to be defective The experimental probability that a student has a birthday during the summer is 17.. Movie; A 7% chance of rain means that it is likely to rain on Thursday, so you should plan to go to a movie.. An unlikely event may occur in any single experiment. Repeating the experiment many times gives a more accurate picture of experimental probabilities.. The event is as likely to happen as not.. There are outcomes for each number cube, any combination of the two cubes will be an outcome of an experiment consisting of rolling two number cubes. So, there are outcomes in the sample space of rolling two standard number cubes. Examples of outcomes (1, 1), (1, ), (1, ) % The experimental probability that a unit produced that day is defective is approximately 1%. Find 1% of. (.1)() 7 There are about 7 units that are likely to be defective. Holt McDougal Algebra 1

14 a The experimental probability that a club is drawn is 7. b The experimental probability that a black suit is drawn summer is 1. test prep 9. B Three outcomes result in a sum of less than, out of possible outcomes.. G residents with pets: ( residents with dogs: ( 1 ) () ) () 1. B x x 1 x 1 x Let h represent the number of times heads occured, and h - represent tails. h + h - h h h h 1 The experimental probability of the coin landing on heads is 1. challenge and extend. There are outcomes in this event (HHH, HHT, HTH, THH) among outcomes in the sample space. This event is as likely as not.. There are outcomes in this event (HHT, HTH, THH) among outcomes in the sample space. This event is unlikely.. There are outcomes in this event (TTH, THT, HTT) among outcomes in the sample space. This event is unlikely.. There is 1 outcome in this event (TTT) among outcomes in the sample space. This event is unlikely. 7a. Coin showing heads: % of.() 1, because there are only two possible outcomes, the number of times the coin shows tails is, -1 7 b. Tossing the coin 1 more times makes the number of trials for this experiment. For experimental probability of tails to be %, find % of 1. Because the coin showed tails 7 times already, the coin must show tails more times for the experimental probability of tails to be %. 1- theoretical probability check it out! 1a. total number of equally likely outcomes. % b. total number of equally likely outcomes. 1 %. P(green) + P(blue) + P(purple) + P(white) P(white) 1. + P(white) P(white).. number of ways event can happen total possible outcomes The probability of winning a free drink is 1. think and discuss 1. Subtract the probability of the event from 1.. P(grey) P(not grey) Odds in favor of grey: 1: Odds against grey: :1 exercises guided practice 1. complement. total number of equally likely outcomes. 1 %. total number of equally likely outcomes. % Holt McDougal Algebra 1

15 . total number of equally likely outcomes. %. total number of equally likely outcomes 1. P(green) + P(red) + P(blue) 1% 1% + % + P(blue) 1% % + P(blue) 1% - % - % P(blue) % 7. P(red) + P(not red) P(not red) P(not red). P(win) + P(not win) P(not win) P(not win) 9 9. P(chosen) + P(not chosen) P(not chosen) P(not chosen) 9 1 number of ways event can happen 1. total possible outcomes The probability of spinner landing on blue is Odds in favor 1:1 The odds in favor of choosing an ace are 1:1. 1. Odds in favor :, or 1: The odds of winning are 1:. number of ways event can happen 1. total possible outcomes The probability of spinner landing on blue is 1. practice and problem solving 1. total number of equally likely outcomes.1 1 % 1. total number of equally likely outcomes. % 1. total number of equally likely outcomes. % 17. P(yellow) + P(not yellow) 1 + P(not yellow) P(not yellow) 9 1. P(win) + P(not win) 1% % + P(not win) 1% - % - % P(not win) 97% 19. P(snow) + P(rain) + P(no snow/rain) 1% 1% + 1% + P(no snow/rain) 1% % + P(no snow/rain) 1% - % - % P(no snow/rain) 7% number of ways event can happen. 99 total possible outcomes 1 The probability of not winning is number of ways event can happen 1. 9 total possible outcomes 1 The probability of not choosing white marble is Odds against 7:, or :1. The odds of the spinner not landing on green are :1.. total number of equally likely outcomes 1. total number of equally likely outcomes 1. total number of equally likely outcomes. Odds in favor of yellow are 1:. 7. Odds against red are :1.. Odds against green are :1. 9. Rolling a number greater than because there are three outcomes in this event (,, ), whereas rolling a number less than has two outcomes (1, ).. Student A; since odds in favor are 1:, there is 1 way the event can happen and ways the event can fail to happen. So the probability of the event not happening is. 1. Odds in favor are the same as odds against: 1:1. So the probability of the event occuring is 1. number of ways event can happen a. total possible outcomes number of ways event can happen b. total possible outcomes 1 number of ways event can happen c. total possible outcomes Holt McDougal Algebra 1

16 . If the odds in favor of an event are a:b, then there is a total of a + b outcomes, where a is number of ways the event can occur. So the probability of the event is a a + b.. area of red circle area of all circles π() π π() π 1 9 test prep. D number of ways event can happen total possible outcomes 7%. H 7. B area of yellow area of entire square P(even) P(less than ) P(not ) P(greater than ) ()() - (1)(1) ()() 9 challenge and extend a. 1. b. 1. c. 1. d. total number of equally likely outcomes 1. e. The experimental probability is closer to the theoretical probability in the experiments with more tosses. 1-7 independent and dependent events Check it out! 1a. Independent; the result of rolling the number cube the 1st time does not affect the result of the nd roll. b. Dependent; choosing the 1st student leaves fewer students to choose from the nd time.. The result of one spin does not affect any following spins. The events are independent. The probability of getting an odd number once is, P(odd) 1 P(odd, odd) P(odd) P(odd) 1. Choose a blue from 1 red, 1 white and blue; Choose a red from 1 red, 1 white and 7 blue; P(blue and red) P(blue) P(red after blue) think and discuss 1. Possible answer: Choosing an ace from a deck of cards and then choosing a king; the events are dependent because the sample space changes after the first card is selected.. Dependent Events Independent Events Example From a bag that has three red marbles and three blue marbles A choosing a red marble B choosing a blue marble A rolling a on a number cube B rolling a on a number cube Probability P(A and B) P(A) P(B after A). 9 1 P(A and B) P(A) P(B) Exercises guided practice 1. dependent. Dependent; the choice of the 1st card affects the sample space for the choice of the nd card.. Independent; the guess for the 1st question does not affect the sample space for the nd question.. Dependent; after you have selected your kitten, there are fewer kittens for your friend to choose from.. Independent; your order does not affect what your friend orders.. Dependent; the appointments that were already scheduled affected the appointment times available to you. 7. The result of one coin toss does not affect any following tosses. The events are independent. The probability of getting heads on first toss is, P(H) P(H, H, H) P(H) P(H) P(H) 1 1. Since the card is replaced, the first card selection does not affect the second selection. The events are independent. Probability of getting odd number on first draw is, P(odd) 7 P(odd, odd) P(odd) P(odd) Holt McDougal Algebra 1

17 9. The result on the first roll does not affect the second roll. The events are independent. Pairs that sum to 7 are: (1, ), (, ), (, ), (, ), (, ), (, 1). All pairs have equal chance of happening. Consider the first pair (1, ). P(1), and P() 1 P(1, ) P(1) P() 1 Similarily the probability of any of the pairs occurring is 1. Since there are pairs, P(sum is 7) P(possible pair with sum is 7) 1. The first roll does not affect the second roll, and neither rolls affect the coin toss. The events are independent. Probability of getting a once is, P(). Probability of getting heads is, P(H). P(,, H) P() P() P(H) The first spin does not affect the second spin. The events are independent. Probability spinner lands on yellow, P(yellow). Probability spinner lands on green, P(green). P(yellow, green) P(yellow) + P(green) Choose a red from red, white and blue; Choose a white from red, white and blue; P(red and white) P(red) P(white after red) Selecting odd from odd and even; Selecting odd from odd and even; P(odd, odd) P(odd) P(odd after odd) Selecting a girl from 1 boys and 1 girls; Selecting a girl from 1 boys and 1 girls; P(girl, girl) P(girl) P(girl after girl) practice and problem solving 1. Dependent; the choice of the first student affects the sample space for the choice of the second student. 1. Independent; the results of rolling the number cube do not affect the sample space of the deck of cards. 17. Neither of the cube roll results affect each other. The events are independent. Probability of rolling even number once is, P(even) 1 P(even, even, even) P(even) P(even) P(even) The first card selection does not affect the second card selection. The events are independent. Probability of selecting even once is, P(even) 1 1 P(even, even) P(even) P(even) The cube roll does not affect the coin toss. The events are independent. Probability of is, P(). Probability of heads is, P(H). P(, H) P() P(H) 1 1. Selecting a red from red, white and blue; Selecting a red from red, white and blue; P(red, red) P(red) P(red after red) Selecting even from even and odd; Selecting even from even and odd; P(even, even) P(even) P(even after even) Holt McDougal Algebra 1

18 . Selecting blue from red, yellow, green, blue, purple and white; Selecting yellow from red, yellow, green, purple and white; P(blue, yellow) P(blue) P(yellow after blue) 1 a. Answering the first question does not affect the sample space for the second or the third questions. The events are independent. Probabililty of answering one question wrong is, P(wrong) P(wrong, wrong, wrong) P(wrong) P(wrong) P(wrong) 7 b. Probability of answering one question right is, P(right) P(right, right, right) P(right) P(right) P(right) 1 1. Independent; the choice of the first name does not affect the sample space for the choice of the second name.. Dependent; the choice of the first name affects the sample space for the choice of the second name.. Independent; the roll of the number cube does not affect the sample space for tossing the coin. 7. Independent; each roll does not affect the sample space for the next roll. a. Number on first die does not affect number on second die, so the events are independent. Probability of getting a on a die is P(). P(, ) P() P() 1 b. The number rolled on either of the dice does not affect the sample space for the rest of the dice, so the events are independent. Probability of getting a on a die is P(). P(,, ) P() P() P() c. The number rolled on either of the dice does not affect the sample space for the rest of the dice, so the events are independent. Probability of getting a on a die is P(). P(,,,, ) P() P() P() P() P() a. Selection of first marble does not affect the sample space for the selection of the second marble, so the events are independent. P(red) ; P(blue) 1 1 P(red, blue) P(red) P(blue) 1 1 b. Selection of first marble affects the sample space for the selection of the second marble, so the events are dependent. Selecting a red from red, blue, white; Selecting a blue from red, blue, white; P(red, blue) P(red) P(blue after red) 1 9 9c. Selection of first marble does not affect the sample space for the selection of the second marble, so the events are independent. P(red) 1 ; P(red, red) P(red) P(red) d. Selection of first marble affects the sample space for the selection of the second marble, so the events are dependent. Selecting a red from red, blue, white; Selecting a red from red, blue, white; P(red, red) P(red) P(red after red) Holt McDougal Algebra 1

19 a. The number rolled on the die does not affect the sample space for the rest of the dice, so the events are independent. Probability of getting a on a die is, P(). Probability for double s on first turn is, P(, ) P() P() 1 Similarly, probability of rolling double s on the second turn is 1. Since the events are independent, P(double sixes on both turns) P(, ) P(, ) b. The number rolled on the die does not affect the sample space for the rest of the dice, so the events are independent. Only pair that sums up to is (1, 1); P(sum ) P(1) P(1) 1 Only pair that sums up to 1 is (, ); P(sum 1) P() P() 1 Since both events of rolling the dice are independent, P(sum, sum 1) P(sum ) P(sum 1) c. The players have the same probability of winning. 1. $. in quarters implies Tamika has 1 quarters. Draw 1 state quarter from state quarters and regular quarters; Draw 1 state quarter from state quarters and regular quarters; P(state, state) P(state) P(state after state) Draw number divisible by from divisible and 7 not divisible by cards; Draw number divisible by from divisible and 7 not divisible by cards; P(divisible by, divisible by ) P(divisible by ) P(divisible by after divisible by ) The probability is because it is impossible for the coin to land heads up on both tosses if it lands on tails on the first toss.. Two events are independent if the occurrence of one event does not affect the probabillity of the other event. test prep. D P(, ) P() P() 1. G P(hit, hit) P(hit) P(hit) A P(man, man) P(man) P(man after man) J P(blue, blue) P(blue) P(blue after blue) challenge and extend 9. Making a throw does not affect the rest of the throws, so the events are independent. P(making, making, making) P(making) P(making) P(making) % 9 Holt McDougal Algebra 1

20 . Rolling a number on the number cube does not affect the sample space for the next roll, so the events are independent. Probability of not getting is, P(not ). Probability of not getting a single is, P(no s) P(not, not, not ) P(not ) P(not ) P(not ) 1 1 P(at least one ) + P(no s) 1 P(at least one ) P(at least one ) %. %. %. % ready to go on? Section B Quiz % % % % %..% The experimental probability that a paper will not have a name on it is.%. Find.% of 17. (.)(17) 11 There are will be 11 papers with no name. 7. total number of equally likely outcomes 1 %. total number of equally likely outcomes 1 9. total number of equally likely outcomes 1 1.% 1. Odds of winning are :9, or 1:19 Odds of winning the prize are 1: number of ways event can happen total possible outcomes 1 % The probability of choosing a winning ticket is %. 1. Odds against are :7. or :7, Odds of no snow are :7. 1. The selection of a captain on one day does not affect the selection of a captain on the next day, so the events are independent. Probability of selecting a girl on the first day is, P(girl) 1 P(girl, girl) P(girl) P(girl) 1 1. % 1. Selecting a scratch-n-sniff sticker from 9 zoo animals and 1 scratch-n-sniff stickers; Selecting a zoo animal sticker from 9 zoo animals and 1 scratch-n-sniff stickers; P(scratch-n-sniff, zoo) P(scratch-n-sniff) P(zoo after scratch-n-sniff) 1 9. % Study Guide: REview 1-1 ORGANIZING AND DISPLAYING DATA 1. outcome. interquartile range. independent events.. 7 boys and girls participated during. Therefore, there were 1 more boys participating. 1- FREQUENCY AND HISTOGRAMS. Stem Leaves Key: 1 means 1 7. Comedy Camp Stem Key: 1 means 1 1 means 1 Days and Days Holt McDougal Algebra 1

21 . The least value is 1. The greatest value is. For this data set use intervals of. Gas Tank Capacities Capacity Tally 1 1 l lll 9 lll 9. Use intervals from the frequency table. Draw a bar for the number of vehicles with given tank capacity in each interval. Gas Tank Capacities 1-1 DATA DISTRIBUTIONS Capacity 1., 7,, 1, 1, 1, 1,, median:, 7,, 1, 1, 1, 1,, The median is 1. mode: 1 range: Median; the mean is higher than four of the prices; the mode is the lowest price. 1.,,, 1, 1, 19, 1,,, 7,,, 9, 1 minimum: ; first quartile: 1 maximum: 1; third quartile: median: MISLEADING GRAPHS AND STATISTICS 1. The scale on the vertical axis is too large. This makes the slopes of the segments less steep. 1. Someone might believe that the price has been relatively stable, when it fact it has doubled. 1- experimental probability % The experimental probability that a battery has no defects is 99.%. 1. Find 99.% of,. (.99)(,),7,7 batteries are likely to have no defects. 17. Find.% of, (.)(,) There are batteries that are likely to have defects. 1- theoretical probability 1. total number of equally likely outcomes total number of equally likely outcomes 1 1. total number of equally likely outcomes 1-7 independent and dependent events 1. The result of the first random number does not affect the result of the second random number, so the events are independent.. The result of the first roll does not affect the result of the second, so the events are independent.. There are fewer people to choose from after the first person is called, so the events are dependent.. Draw a yellow from green, 1 yellow, 1 gold and silver; Draw a green from green, 17 yellow, 1 gold and silver; P(yellow, green) P(yellow) P(green after yellow) Draw a gold from green, 1 yellow, 1 gold and silver; Draw a gold from green, 1 yellow, gold and silver; P(gold, gold) P(gold) P( gold after gold) The draw of the first ball does not affect the draw of the second ball, so events are independent. P(green, green) P(green) P(green) Holt McDougal Algebra 1

22 chapter test 1. A line graph is appropriate for this data because it will show the change in population over a period of time. Oakville Population Population, 1, 1,,. from 197 to Year. The population is decreasing, but by smaller amounts as time passes.. Stem Leaves Key: 1 means 1. The least value is 1. The greatest value is 7. For this data set use intervals of. High Temperature for Two Weeks Temperatures ( F) Tally 1 ll ll 9 lll 7 7 ll. Use intervals from the frequency table. Draw a bar for the number of frequencies of the temperatures in each interval. High Temperature for Two Weeks. minimum: ; first quartile: maximum: ; third quartile: % The experimental probability that a watch has no defects is 99.%. 1. Find 99.% of,. (.99)(,) 9, 9, watches are likely to have no defects. 11. The sectors of the graph do not add up to 1%. The total of the percentage is only %. 1. Someone might believe that most of the money raised goes to charitable causes. 1. Possible answer: the managers of the charity might be able to get moere people to contribute under the invalid assumption that most of their money is going to charitable causes. 1. total number of equally likely outcomes 1 1 number of ways event can happen 1. 7 total possible outcomes 9 The probability of not spinning red is Selecting white from 1 red and 1 white marbles; Selecting white from 1 red and 9 white marbles; P(white, white) P(white) P(white after white) Temperature ( F) median:,,,,, 1, 1, 1, 1, 17, 1,,, The median is 1.. mode: 1 range: - Holt McDougal Algebra 1