Algebra 1A. Unit 05 GUIDED NOTES

Transcription

1 Algebra 1A Unit 0 Sections 1.9, 2., 2. GUIDED NOTES NAME Teacher Period 1 1

2 Section 1-9: Analyzing Tables and Graphs Notes Date: Why are graphs used to display data? Why are tables used to display data? Example 1: Use the graph to answer the questions. a) Describe how you can tell from the graph that the number of men in NCAA sports remained about the same, while the number of women increased? b) Approximately how many more men than women participated in sports during the school year? c) Which is better to use to answer part b the graph or the table? d) What was the total participation among men and women in the academic year? e) Why did you need to use the table to answer part d? 2 2

3 Example 2: A recent poll in New York asked residents whether cell phone use while driving should be banned. The results are show in the circle graph. a) If 20 people in New York were surveyed, about how many would think that cell phone use while driving should be banned? Show all work. b) If a city of 1,000 is representative of those surveyed, how many people could be expected not to know whether cell phone use while driving should be banned? Show all work. Example 3: Use the graph to answer the questions. a) How would the change in enrollment between 1997 and 1999 compare to the change in enrollment between 199 and 1999? Show all work. b) Why can t you simply extend the line on the graph beyond 1999 to predict the number of students enrolled in 200? Example : Joel used the graph below to show his algebra grade for the first four reporting periods of the year. Does the graph misrepresent the data? Explain in sentences. 3 3

4 Date: Section 2-: Displaying and Analyzing Data Notes Part 1 1. What was the most popular boys name in all five decades? 2. How can you tell? 3. Were any girls names as popular as Michael?. How can you tell? Example 1: Draw a line plot for the data. Which number occurs the most frequently? 11, - 2, 10, -2, 7, 2, 7,, 9, 0,, 9, 7, 2, 0,, 10, 7,, 9 Example 2: The highway patrol did a radar survey of the speeds of cars along a stretch of highway for 1 minute. The speeds (in miles per hour) of the 20 cars that passed are listed below. 72, 70, 72, 7, 8, 9, 70, 72, 7, 7, 79, 7, 7, 72, 70,, 9,, 8, 7 a) Make a line plot of the data. b) Which speed occurs the most frequently?

5 Example 3: Use the data below to make a stem and leaf plot. 8, 78, 100, 99, 108, 11, 131, 121, 11, 93, 12, 11, 123, 79, 8, 92, 92, 131, 90, 7, 10, 8, 88, 110, 70, 107, 11, 97, 129, 132 Example : Monique wants to compare the monthly average high temperatures of Dallas and Atlanta before she decides which city she wants to move. The table shows the monthly average high temperatures for both cities. a) Make a stem and leaf plot to compare the data. b) What is the difference between the highest average temperatures in each city? c) Which city has higher average temperatures?

6 Date: Section 2-: Displaying and Analyzing Data Notes Part 2 Measures of Central Tendency: Mean: Median: Mode: Example 1: The numbers below show the ages of the US Presidents since 1900 at the time they were inaugurated. Which measure of central tendency best represents the data? Show all work. Example 2: Which measure of central tendency best represents the data? Show all work.

7 Example 3: The number of electoral votes for the 12 most populous states in the 2000 Presidential election are listed below. Which measure of central tendency best represents the data? Show all work. 21, 22, 18, 23, 1, 2, 1, 32, 13, 33, 13, Example : Which measure of central tendency best represents the data? Show all work. 7 7

8 Date: Section 2-: Probability: Simple Probability and Odds Notes Part 1 PROBABILITY: Probability Simple Event Sample Space Example 1: Find the probability of rolling a on a die. Example 2: Find the probability of rolling a number greater than two on a die. Example 3: Find the probability of rolling an even number on a die. Example : A class contains students with black hair, 8 with brown hair, four with blonde hair and two with red hair. Find P (black). Example : A class contains students with black hair, 8 with brown hair, four with blonde hair and two with red hair. Find P (red or brown). 8 8

9 Example : A class contains students with black hair, 8 with brown hair, four with blonde hair and two with red hair. Find P (not blonde). Example 7: A bowl contains red chips, 7 blue chips, yellow chips and 10 green chips. One chip is randomly drawn. Find the probability that the chip is blue. Example 8: A bowl contains red chips, 7 blue chips, yellow chips and 10 green chips. One chip is randomly drawn. Find P (red or yellow). Example 9: A bowl contains red chips, 7 blue chips, yellow chips and 10 green chips. One chip is randomly drawn. Find the probability that the chip is not green. 9 9

10 Date: Section 2-: Probability: Simple Probability and Odds Notes Part 2 ODDS: Odds: Example 1: Find the odds of rolling a number less than 3 on a die. Example 2: Find the odds of rolling a number greater than 2 on a die. Example 3: A weather forecast states that the probability of rain the next day is 0%. What are the odds that it will rain? 10 10

11 Example : Melvin is waiting to board a flight to Washington, DC. According to the airline, the flight he is waiting for is on time 80% of the time it flies. What are the odds that the plane will be on time? Example : A card is selected at random from a standard deck of 2 cards. What are the odds against selecting a 3? Example : A card is selected at random from a standard deck of 2 cards. What are the odds against selecting a 2 or a? 11 11

12 1-9 NAME DATE PERIOD Study Guide and Intervention Statistics: Analyzing Data by Using Tables and Graphs Analyze Data Graphs or tables can be used to display data. A bar graph compares different categories of data, while a circle graph compares parts of a set of data as a percent of the whole set. A line graph is useful to show how a data set changes over time. Example The circle graph at the right shows the number of international visitors to the United States in 2000, by country. International Visitors to the U.S., 2000 a. If there were a total of 0,891,000 visitors, how many were from Mexico? 0,891,000 20% 10,178,200 b. If the percentage of visitors from each country remains the same each year, how many visitors from Canada would you expect in the year 2003 if the total is 9,000,000 visitors? 9,000,000 29% 17,110,000 Others 32% United Kingdom 9% Japan 10% Source: TInet Canada 29% Mexico 20% Exercises 1. The graph shows the use of imported steel by U. S. companies over a 10-year period. a. Describe the general trend in the graph. The general trend is an increase in the use of imported steel over the 10-year period, with slight decreases in 199 and b. What would be a reasonable prediction for the percentage of imported steel used in 2002? about 30% Percent Imported Steel as Percent of Total Used Year Source: Chicago Tribune Lesson The table shows the percentage of change in worker productivity at the beginning of each year for a -year period. a. Which year shows the greatest percentage increase in productivity? 1998 b. What does the negative percent in the first quarter of 2001 indicate? Worker productivity decreased in this period, as compared to the productivity one year earlier. Worker Productivity Index Year (1st Qtr.) % of Change Source: Chicago Tribune Glencoe/McGraw-Hill 9 Glencoe Algebra 1 12

13 1-9 NAME DATE PERIOD Study Guide and Intervention (continued) Statistics: Analyzing Data by Using Tables and Graphs Misleading Graphs Graphs are very useful for displaying data. However, some graphs can be confusing, easily misunderstood, and lead to false assumptions. These graphs may be mislabeled or contain incorrect data. Or they may be constructed to make one set of data appear greater than another set. Example The graph at the right shows the number of students per computer in the U.S. public schools for the school years from 199 to Explain how the graph misrepresents the data. The values are difficult to read because the vertical scale is too condensed. It would be more appropriate to let each unit on the vertical scale represent 1 student rather than students and have the scale go from 0 to 12. Students per Computer, U.S. Public Schools 20 Students Years since 199 Source: The World Almanac Exercises Explain how each graph misrepresents the data. 1. The graph below shows the U.S. 2. The graph below shows the amount of greenhouse gases emissions for money spent on tourism for Nitrous Oxide % Methane 9% HCFs, PFCs, and Sulfur Hexafluoride 2% U.S. Greenhouse Gas Emissions 1999 Carbon Dioxide 82% World Tourism Receipts 0 Billions of $ Year Source: The World Almanac Source: Department of Energy The graph is misleading because the sum of the percentages is not The graph is misleading because the vertical axis starts at %. Another section needs to be added to account for the billion. This gives the impression that $00 billion is a minimum missing 1%, or 3.. amount spent on tourism. Glencoe/McGraw-Hill 0 Glencoe Algebra 1 13

14 1-9 NAME DATE PERIOD Skills Practice Statistics: Analyzing Data by Using Tables and Graphs DAILY LIFE For Exercises 1 3, use the circle graph that shows the percent of time Keisha spends on activities in a 2-hour day. 1. What percent of her day does Keisha spend in the combined activities of school and doing homework? 0% 2. How many hours per day does Keisha spend at school? 9 h 3. How many hours does Keisha spend on leisure and meals? 3 h Keisha s Day Sleep 37.% School 37.% Meals 8% Homework 12.% Leisure.% PASTA FAVORITES For Exercises 8, use the table and bar graph that show the results of two surveys asking people their favorite type of pasta. Spaghetti Fettuccine Linguine Survey Survey Spaghetti Fettucine Linguine 0 Pasta Favorites Number of People Survey 1 Survey 2. According to the graph, what is the ranking for favorite pasta in both surveys? The ranking is the same for both: spaghetti, fettuccine, linguine.. In Survey 1, the number of votes for spaghetti is twice the number of votes for which pasta in Survey 2? linguine. How many more people preferred spaghetti in Survey 2 than preferred spaghetti in Survey 1? 10 people 7. How many more people preferred fettuccine to linguine in Survey 1? people Lesson If you want to know the exact number of people who preferred spaghetti over linguine in Survey 1, which is a better source, the table or the graph? Explain. The table, because it gives exact numbers. PLANT GROWTH For Exercises 9 and 10, use the line graph that shows the growth of a Ponderosa pine over years. 9. Explain how the graph misrepresents the data. The vertical axis begins at 10, making it appear that the tree grew much faster compared to its initial height than it actually did. 10. How can the graph be redrawn so that it is not misleading? To reflect accurate proportions, the vertical axis should begin at 0. Height (ft) Growth of Pine Tree Years Glencoe/McGraw-Hill 1 Glencoe Algebra 1 1

15 1-9 NAME DATE PERIOD Practice (Average) Statistics: Analyzing Data by Using Tables and Graphs MINERAL IDENTIFICATION For Exercises 1, use the following information. The table shows Moh s hardness scale, used as a guide to help identify minerals. If mineral A scratches mineral B, then A s hardness number is greater than B s. If B cannot scratch A, then B s hardness number is less than or equal to A s. 1. Which mineral(s) will fluorite scratch? talc, gypsum, calcite 2. A fingernail has a hardness of 2.. Which mineral(s) will it scratch? talc, gypsum 3. Suppose quartz will not scratch an unknown mineral. What is the hardness of the unknown mineral? at least 7. If an unknown mineral scratches all the minerals in the scale up to 7, and corundum scratches the unknown, what is the hardness of the unknown? between 7 and 9 Mineral Hardness Talc 1 Gypsum 2 Calcite 3 Fluorite Apatite Orthoclase Quartz 7 Topaz 8 Corundum 9 Diamond 10 SALES For Exercises and, use the line graph that shows CD sales at Berry s Music for the years Which one-year period shows the greatest growth in sales? from 1999 to Describe the sales trend. Sales started off at about 000 in 1998, then dipped in 1999, showed a sharp increase in 2000, then a steady increase to Total Sales (thousands) CD Sales Year MOVIE PREFERENCES For Exercises 7 9, use the circle graph that shows the percent of people who prefer certain types of movies. 7. If 00 people were surveyed, how many chose action movies as their favorite? Of 1000 people at a movie theater on a weekend, how many would you expect to prefer drama? What percent of people chose a category other than action or drama? 2.% TICKET SALES For Exercises 10 and 11, use the bar graph that compares annual sports ticket sales at Mars High. 10. Describe why the graph is misleading. Beginning the vertical axis at 20 instead of 0 makes the relative sales for volleyball and track and field seem low. 11. What could be done to make the graph more accurate? Start the vertical axis at 0. Movie Preferences Drama 30.% Foreign 0.% Tickets Sold (hundreds) Action % Comedy 1% Science Fiction 10% Ticket Sales Basketball Football Track & Field Volleyball Glencoe/McGraw-Hill 2 Glencoe Algebra 1 1

16 2- NAME DATE PERIOD Study Guide and Intervention Statistics: Displaying and Analyzing Data Create Line Plots and Stem-and-Leaf Plots One way to display data graphically is with a line plot. A line plot is a number line labeled with a scale that includes all the data and s placed above a data point each time it occurs in the data list. The s represent the frequency of the data. A stem-and-leaf plot can also be used to organize data. The greatest common place value is called the stem, and the numbers in the next greatest place value form the leaves. Example 1 Example 2 Draw a line plot for the data Step 1 The value of the data ranges from 3 to 10, so construct a number line containing those points Step 2 Then place an above the number each time it occurs Exercises Use the data below to create a stem-and-leaf plot The greatest common place value is tens, so the digits in the tens place are the stems. Thus 2 would have a stem of and 10 would have a stem of ten. The stem-and-leaf plot is shown below. Stem Leaf Use the table at the right for Exercises Make a line plot representing the weights of the wrestlers shown in the table at the right. Weights of Junior Varsity Wrestlers (pounds) How many wrestlers weigh over 10 lb? 3. What is the greatest weight? Use each set of data to make a stem-and-leaf plot Lesson 2- Glencoe/McGraw-Hill 99 Glencoe Algebra 1 1

17 2- Analyze Data Numbers that represent the centralized, or middle, value of a set of data are called measures of central tendency. Three measures of central tendency are the mean, median, and mode. Mean Definition Sum of the data values divided by the number of values in the data set. Example Data: 2, 3, 21, 30, 21, 30; 27 The middle number in a data set when the numbers are arranged in numerical Median order. If there is an even number of 2 30 Data: 21, 21, 2, 30, 31, 2; values, the median is halfway between the two middle values. Mode NAME DATE PERIOD Study Guide and Intervention (continued) Statistics: Displaying and Analyzing Data The number or numbers that occur most often in the set of data. Data: 21, 21, 2, 30, 30, 3; 21 and 30 are modes Example Which measure of central tendency best represents the data? Stem Leaf Find the mean, median, and mode. Mean 10 Median 102 Modes 99 and 112 The median best represents the center of the data since the mean is too high. Exercises Find the mean, median, and mode for each data set. Then tell which best represents the data Stem Leaf Stem Leaf Stem Leaf Month Days above 90. May June 7 July 1 August 12 September Glencoe/McGraw-Hill 100 Glencoe Algebra 1 17

18 2- NAME DATE PERIOD Skills Practice Statistics: Displaying and Analyzing Data Use each set of data to make a line plot INCOME For Exercises 3, use the list that shows the income from each assignment for a private investigator for a year. 3. Make a line plot of the data What was the median income per assignment for the investigator?. Does the median best represent the data? Use each set of data to make a stem-and-leaf plot Stem Leaf Stem Leaf EMPLOYMENT For Exercises 8 10, use the list that shows the ages of employees at Watson & Sterling Publications Make a stem-and-leaf plot of the data. 9. Which age occurs most frequently? 10. Does the mode best represent the data? Explain. Stem Leaf Lesson 2- Glencoe/McGraw-Hill 101 Glencoe Algebra 1 18

19 2- Use each set of data to make a line plot NAME DATE PERIOD Practice Statistics: Displaying and Analyzing Data HEALTH For Exercises 3 and, use the list that shows the grams of saturated fat in a serving of a variety of grains such as bread, cereal, crackers, and pasta. 3. Make a line plot of the data Which measure of central tendency best describes the data? Explain. Use each set of data to make a stem-and-leaf plot Stem Leaf EMPL0YMENT For Exercises 7 10, use the lists that show survey results of students time spent on the Internet and on the telephone for a month. Internet Stem Leaf Telephone Make a stem-and-leaf plot to compare the data. 8. Which value appears most frequently in each set of data? 9. Is the mode the best measure to compare the data? 10. Overall, did students spend more time on the Internet or the telephone? Internet Stem Telephone Glencoe/McGraw-Hill 102 Glencoe Algebra 1 19

20 2- NAME DATE PERIOD Reading to Learn Mathematics Statistics: Displaying and Analyzing Data Pre-Activity How are line plots and averages used to make decisions? Read the introduction to Lesson 2- at the top of page 88 in your textbook. What was the number one name for boys in all five decades? Look at the decade in which you were born. Is your name or the names of any of the other students in your class in the top five for that decade? Reading the Lesson 1. Use the line plot shown below to answer the questions a. What are the data points for the line plot? b. What do the three s above the represent? 2. Explain what is meant by the frequency of a data number. 3. Use the stem-and-leaf plot shown at the right. a. How is the number 78 represented on the plot? b. Explain how you know there are 23 numbers in the data. Stem Leaf Helping You Remember. Describe how you would explain the process of finding the median and mode from a stem-and-leaf plot to a friend who missed Lesson 2-. Lesson 2- Glencoe/McGraw-Hill 103 Glencoe Algebra 1 20

21 2- NAME DATE PERIOD Enrichment Runs Created In The 1978 Bill James Baseball Abstract, the author introduced the runs created formula. R (h + w)t (b + w) where for each player h number of hits w number of walks, t number of total bases, b number of at-bats, and R approximate number of runs a team scores due to this player s actions 1. As of June 29, 2001, Roberto Alomar of the Cleveland Indians and Seattle Mariners player Ichiro Suzuki were tied with the highest American League batting average at.31. Find the number of runs created by each player using the data below. h w t b Runs Created Alomar Suzuki Based on this information, who do you think is the more valuable American League player? Why? 2. Carlos Lee of the Chicago White Sox and New York Yankee Bernie Williams were both batting.31. Find the number of runs created by each player using the data below. h w t b Runs Created Lee Williams Why would baseball teams want to calculate the number of runs created by each of their players? Glencoe/McGraw-Hill 10 Glencoe Algebra 1 21

22 2- NAME DATE PERIOD Study Guide and Intervention Probability: Simple Probability and Odds Probability The probability of a simple event is a ratio that tells how likely it is that the event will take place. It is the ratio of the number of favorable outcomes of the event to the number of possible outcomes of the event. You can express the probability either as a fraction, as a decimal, or as a percent. number of favorable outcomes Probability of a Simple Event For an event a, P(a). number of possible outcomes Lesson 2- Example 1 Example 2 Mr. Babcock chooses out of 2 students in his algebra class at random for a special project. What is the probability of being chosen? number of students chosen P(being chosen) total number of students 1 The probability of being chosen is or. 2 Exercises A bowl contains 3 pears, bananas, and 2 apples. If you take a piece of fruit at random, what is the probability that it is not a banana? There are 3 2 or 9 pieces of fruit. There are 3 2 or pieces of fruit that are not bananas. number of other pieces of fruit P(not banana) total number of pieces of fruit 9 The probability of not choosing a banana is. 9 A card is selected at random from a standard deck of 2 cards. Determine each probability. 1. P(10) 2. P(red 2) 3. P(king or queen). P(black card). P(ace of spades). P(spade) Two dice are rolled and their sum is recorded. Find each probability. 7. P(sum is 1) 8. P(sum is ) 9. P(sum is less than ) 10. P(sum is greater than 11) 11. P(sum is less than 1) 12. P(sum is greater than 8) A bowl contains red chips, 3 blue chips, and 8 green chips. You choose one chip at random. Find each probability. 13. P(not a red chip) 1. P(red or blue chip) 1. P(not a green chip) A number is selected at random from the list {1, 2, 3,, 10}. Find each probability. 1. P(even number) 17. P(multiple of 3) 18. P(less than ) 19. A computer randomly chooses a letter from the word COMPUTER. Find the probability that the letter is a vowel. Glencoe/McGraw-Hill 10 Glencoe Algebra 1 22

23 2- NAME DATE PERIOD Study Guide and Intervention (continued) Probability: Simple Probability and Odds Odds The odds of an event occurring is the ratio of the number of ways an event can occur (successes) to the number of ways the event cannot occur (failures). Odds number of successes number of failures Example A die is rolled. Find the odds of rolling a number greater than. The sample space is {1, 2, 3,,, }. Therefore, there are six possible outcomes. Since and are the only numbers greater than, two outcomes are successes and four are failures. 2 So the odds of rolling a number greater than is, or 1:2. Exercises Find the odds of each outcome if the spinner at the right is spun once. 1. multiple of 2. odd number 3. even or a. less than even number greater than Find the odds of each outcome if a computer randomly chooses a number between 1 and 20.. the number is less than the number is a multiple of 8. the number is even 9. the number is a one-digit number A bowl of money at a carnival contains 0 quarters, 7 dimes, 100 nickels, and 12 pennies. One coin is randomly selected. 10. Find the odds that a dime will not be chosen. 11. What are the odds of choosing a quarter if all the dimes are removed? 12. What are the odds of choosing a penny? Suppose you drop a chip onto the grid at the right. Find the odds of each outcome. 13. land on a shaded square 1. land on a square on the diagonal land on square number 1 1. land on a number greater than land on a multiple of Glencoe/McGraw-Hill 10 Glencoe Algebra 1 23

24 2- NAME DATE PERIOD Skills Practice Probability: Simple Probability and Odds One chip is randomly selected from a jar containing 8 yellow chips, 10 blue chips, 7 green chips, and red chips. Find each probability. 1. P(blue) 2. P(green) 3. P(yellow or green). P(blue or yellow) Lesson 2-. P(not red). P(not blue) Find the probability of each outcome if the spinner is spun once. 7. P(multiple of 3) 8. P(less than 7) 9. P(odd or 2) 10. P(not 1) A person is born in the month of June. Find each probability. 11. P(date is a multiple of ) 12. P(date is before June 1) 13. P(before June 7 or after June 2) 1. P(not after June ) Find the odds of each outcome if a computer randomly picks a letter in the name The Petrified Forest. 1. the letter f 1. the letter e 17. the letter t 18. a vowel CLASS SCHEDULES For Exercises 19 22, use the following information. A student can select an elective class from the following: 3 in music, in physical education, 2 in journalism, 8 in computer programming, in art, and in drama. Find each of the odds if a student forgets to choose an elective and the school assigns one at random. 19. The class is computer programming. 20. The class is drama. 21. The class is not physical education. 22. The class is not art. Glencoe/McGraw-Hill 107 Glencoe Algebra 1 2

25 2- NAME DATE PERIOD One chip is randomly selected from a jar containing 13 blue chips, 8 yellow chips, 1 brown chips, and green chips. Find each probability. 1. P(brown) 2. P(green) 3. P(blue or yellow). P(not yellow) A card is selected at random from a standard deck of 2 cards. Find each probability.. P(heart). P(black card) 7. P(jack) 8. P(red jack) Two dice are rolled and their sum is recorded. Find each probability. 9. P(sum less than ) 10. P(sum less than 2) 11. P(sum greater than 10) 12. P(sum greater than 9) Find the odds of each outcome if a computer randomly picks a letter in the name The Badlands of North Dakota. 13. the letter d 1. the letter a 1. the letter h 1. a consonant CLASS PROJECTS For Exercises 17 20, use the following information. Students in a biology class can choose a semester project from the following list: animal behavior (), cellular processes (2), ecology (), health (7), and physiology (3). Find each of the odds if a student selects a topic at random. 17. the topic is ecology 18. the topic is animal behavior 19. the topic is not cellular processes 20. the topic is not health SCHOOL ISSUES For Exercises 21 and 22, use the following information. A news team surveyed students in grades 9 12 on whether to change the time school begins. One student will be selected at random to be interviewed on the evening news. The table gives the results. 21. What is the probability the student selected will be in the 9th grade? Practice Probability: Simple Probability and Odds 22. What are the odds the student selected wants no change? Grade No change 2 3 Hour later Glencoe/McGraw-Hill 108 Glencoe Algebra 1 2

26 2- NAME DATE PERIOD Reading to Learn Mathematics Probability: Simple Probability and Odds Pre-Activity Why is probability important in sports? Read the introduction to Lesson 2- at the top of page 9 in your textbook. Look up the definition of the word probability in a dictionary. Rewrite the definition in your own words. Lesson 2- Reading the Lesson 1. Write whether each statement is true or false. If false, replace the underlined word or number to make a true statement. a. Probability can be written as a fraction, a decimal, or a percent. b. The sample space of flipping one coin is heads or tails. c. The probability of an impossible event is 1. d. The odds against an event occurring are the odds that the event will occur. 2. Explain why the probability of an event cannot be greater than 1 while the odds of an event can be greater than 1. Helping You Remember 3. Probabilities are usually written as fractions, decimals, or percents. Odds are usually written with a colon (for example, 1:3). How can the spelling of the word colon help remember this? Glencoe/McGraw-Hill 109 Glencoe Algebra 1 2

27 NAME DATE PERIOD 2- Enrichment Geometric Probability If a dart, thrown at random, hits the triangular board shown at the right, what is the probability that it will hit the shaded region? This can be determined by comparing the area of the shaded region to the area of the entire board. This ratio indicates what fraction of the tosses should hit in the shaded region. area of shaded region area of triangular board 1 2 ()() 1 2 (8)() 12 2 or 1 2 In general, if S is a subregion of some region R, then the probability, P(S), that a point, chosen at random, belongs to subregion S is given by the following: P(S) area of subregion S area or region R Find the probability that a point, chosen at random, belongs to the shaded subregions of the following figures Glencoe/McGraw-Hill 110 Glencoe Algebra 1 27