Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Slide 3 / 241 Slide 4 / 241 Table of Contents click on the topic to go to that section Sets Independence and Conditional Probability Permutations & Combinations Sets Measures of Central Tendency Standard Deviation and Normal Distribution Two-Way Frequency Tables Sampling and Experiments Return to Table of Contents Slide 5 / 241 Slide 6 / 241 Why do we need this? Goals and Objectives Students will be able to use characteristics of problems, including Being able to categorize and describe situations allows us to unions, intersections and complement, to describe events with analyze problems that we are presented with in their most basic appropriate set notation and Venn Diagrams. forms. Many different fields need to categorize elements they use or study. Businesses need to look at what they are offering, Biologists need to organize material they are studying and even you will need to categorize different options for your living situation, such as insurance, in the future.
Slide 7 / 241 Slide 8 / 241 Create a Venn Diagram to match the Vocabulary and Set Notation information. Sample Space - Set of all possible outcomes. U 4 Universe (U) - Set of all elements that need to be considered 7 A 2 B in the problem. 9 0 Empty Set ( ∅ ) - The set that has no elements. 10 8 1 Subset - a set that is a part of a larger set. 6 5 3 Sets are usually denoted with uppercase letters and listed with brackets. For example: A = {-5, -2, 0, 1, 5} A = {0, 2, 3, 7, 9} B = {1, 3, 7, 10} U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Slide 8 (Answer) / 241 Slide 9 / 241 Create a Venn Diagram to match the Data Displays information. Venn Diagrams are one example of a sample space that helps us organize information.You can also use charts, tables, graphs and tree diagrams just to name a few more. U Teacher Notes Move the circles and 4 7 A 2 B Tree Diagram for tossing a coin 3 times: Chart for rolling 2 dice (sums): numbers around to 9 H 0 mirror the given 6 7 8 9 10 11 12 H information. T 10 5 6 7 8 9 10 11 H H 8 4 5 6 7 8 9 10 1 T T 6 4 5 6 7 8 9 3 5 H 4 5 6 7 8 3 2 3 H T [This object is a pull tab] 2 3 4 5 6 7 T 1 A = {0, 2, 3, 7, 9} H T 5 6 1 2 3 4 B = {1, 3, 7, 10} T U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Slide 10 / 241 Slide 10 (Answer) / 241 Data Displays Data Displays Use a sample space that helps organize the data effectively. Use a sample space that helps organize the data effectively. 1. Venn Diagram or chart 2. Chart 3. Venn Diagram or chart For example, would you be able to effectively For example, would you be able to effectively Teacher Notes 4. Venn Diagram or chart display a coin toss in a Venn Diagram or on display a coin toss in a Venn Diagram or on a chart? Decide how to display the following a chart? Decide how to display the following There can be different answers. information. information. This question brings up other concerns such as how many people were asked and other parameters we will address in the unit. 1. Survey results about what subject students like in school. 1. Survey results about what subject students like in school. [This object is a pull tab] 2. The different ways you can deal two cards from a deck of cards. 2. The different ways you can deal two cards from a deck of cards. 3. Results that compare the number of men and women that like 3. Results that compare the number of men and women that like chocolate ice cream over vanilla ice cream. chocolate ice cream over vanilla ice cream. 4. A poll on which grocery store people prefer to go to. 4. A poll on which grocery store people prefer to go to.
Slide 11 / 241 Slide 11 (Answer) / 241 The Universe The Universe The Universe (U) is all aspects that should be considered in a The Universe (U) is all aspects that should be considered in a 1. Women that are enrolled as students at situation. The Universe (U) is basically the same as a sample situation. The Universe (U) is basically the same as a sample that particular college. space also used in probability. space also used in probability. Teacher Notes 2. The deck of cards 3. People in the United States that not only Name the Universe (U) of the following: Name the Universe (U) of the following: picked up their phone, but answered the question. 1. Survey at a local college asking women what they are 1. Survey at a local college asking women what they are studying. studying. The term "Universe" is more often used in set theory while "sample 2. Calculating the probability that you would draw a red 2. Calculating the probability that you would draw a red space" is used with probability. 10 out of a deck of cards. 10 out of a deck of cards. [This object is a pull tab] 3. Phone survey on who you will vote for in the U. S. 3. Phone survey on who you will vote for in the U. S. Presidential race. Presidential race. Slide 12 / 241 Slide 13 / 241 Empty Set Example U A B -3 6 The Empty Set ( ∅ ) is the equivalent of zero when referring to sets. -2 17 7 For example, if you asked people at a college their age, the number -12 5 of people that answered "2 years old" would be ∅ . 3 4 1 An example of a subset would be the numbers 2, -6, and 13 in the -1 0 set of integers. 15 C An outcome is a result of an experiment or survey. 1. List the universe for this problem. 2. Name the different sets involved. 3. Find the subset that is in both A and B. 4. Find the subset that is in all sets A, B and C. Slide 13 (Answer) / 241 Slide 14 / 241 Example 1 What is most likely the Universe of the following situation? A U = {men} U A B B U = {women} -3 C U = {people} 6 -2 17 7 D U = {people at a fitness club} -12 E U = {people exercising at home} 5 3 1. U = {-12, -3, -2, -1, 0, 1, 3, 4, 5, 6, 7, 15, 17} 4 1 2. A = {-3, -2, 1, 5} Women Men B = {-3, 4, 5, 6} Answer C = {0, 1, 4, 5, 15} -1 0 *3. A∩B = {-3, 5} 15 C *4. A∩B∩C = {5} 6am aerobics 4pm water 5pm cycling 1. List the universe for this problem. *note: the notation and concept of intersection 10am weight aerobics will be dealt with in the next section of the unit. lifting 2. Name the different sets involved. 3. Find the subset that is in both A and B. 3pm nutrition 7pm weight lifting 4. Find the subset that is in all sets A, B and C. 2pm climbing [This object is a pull tab] 6pm swimming
Slide 14 (Answer) / 241 Slide 15 / 241 2 What is the most popular activity, or activities, at the club? 1 What is most likely the Universe of the following situation? *Answer as many letters as necessary. A U = {men} Women Men B U = {women} A 6 am aerobics C U = {people} 6am aerobics B 4 pm water aerobics D U = {people at a fitness club} 4pm water 5pm cycling C 3 pm nutrition E U = {people exercising at home} 10am weight aerobics lifting D 5 pm cycling 3pm nutrition E 10 am weight lifting 7pm weight lifting Women Men Answer F 2 pm climbing 2pm climbing 6pm swimming D G 6 pm swimming 6am aerobics H 7 pm weight lifting 4pm 5pm cycling water I Not enough information to tell 10am weight aerobics lifting 3pm nutrition 7pm weight lifting 2pm climbing [This object is a pull tab] 6pm swimming Slide 15 (Answer) / 241 Slide 16 / 241 2 What is the most popular activity, or activities, at the club? 3 What are the most popular activities for both men and *Answer as many letters as necessary. women at the club? Men Women Women Men I or all of A through H. A 5 pm cycling A 6 am aerobics Answer 6am aerobics You need actual 6am aerobics B 4 pm water aerobics 4pm B 4 pm water aerobics 4pm numbers to tell what is 5pm cycling water C 6 am aerobics 5pm cycling water 10am weight C 3 pm nutrition aerobics 10am weight most popular or a better aerobics lifting lifting D 10 am weight lifting D 5 pm cycling explanation of what the 3pm nutrition 7pm weight lifting 3pm nutrition E 7 pm weight lifting E 10 am weight lifting 7pm weight lifting diagram is about. F 3 pm nutrition 2pm climbing F 2 pm climbing 2pm climbing 6pm swimming 6pm swimming G 6 pm swimming G 6 pm swimming [This object is a pull tab] H 2 pm climbing H 7 pm weight lifting I Not enough information to tell I Not enough information to tell Slide 16 (Answer) / 241 Slide 17 / 241 4 What is the best display for the sample space (or 3 What are the most popular activities for both men and universe) of rolling an odd number on a single number women at the club? Women Men cube? 4 pm water aerobics A 5 pm cycling Answer 6am aerobics Answer B 4 pm water aerobics 4pm A S = {1, 2, 3, 4, 5, 6} water 3 pm nutrition 5pm cycling # C 6 am aerobics 10am weight aerobics D lifting 1 1 D 10 am weight lifting 2 3pm nutrition 2 7pm weight lifting E 7 pm weight lifting 3 3 B 4 F 3 pm nutrition 2pm climbing 4 6pm swimming 5 G 6 pm swimming [This object is a pull tab] 5 6 6 H 2 pm climbing I Not enough information to tell 4 1 E 5 C S = {1, 3, 5} 6 2 3
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