COMPOUND EVENTS. Judo Math Inc.


 Blake Richard
 2 years ago
 Views:
Transcription
1 COMPOUND EVENTS Judo Math Inc.
2 7 th grade Statistics Discipline: Black Belt Training Order of Mastery: Compound Events 1. What are compound events? 2. Using organized Lists (7SP8) 3. Using tables (7SP8) 4. Using tree diagrams (7SP8) 5. Choose your method 6. Using simulation (7SP8) Welcome to the Black Belt Last discipline you learned a lot about probability OR the likelihood that an event will occur. You did a lot of work with dice, spinners, pennies, etc to try to predict certain outcomes. We also realized that we can figure out the mathematical likelihood that something will happen (theoretical probability), but that may be different from what actually happens when you conduct the experiment (experimental likelihood). In this, your last and final belt packet, you are going to do some modeling with probability situations that are a little more challenging. These situations are called compound events and instead of asking questions about one thing going on, we are going to ask questions about two things going on like two dice, or two spinners, or even more crazy things! In seventh grade, you are just going to do a lot of modeling and experimenting with this, but as you move to 8, 9 and 10 grade you will learn a lot more of the math behind compound events (or you can google it right now and start learning more about it!) In this discipline you are going to learn 4 different methods of understanding probability of compound events and determining the sample space of the event. My favorite is the tree diagram pictured here to the right, but you will have to decide for yourself which modeling tool works best for your amazing brain! Good luck grasshopper. Standards Included: 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. 7.SP.8c Design and use a simulation to generate frequencies for compound events. Judo Math Inc.
3 1. What are compound events? Compound events are the combined probability of two or more events. Independent Events Dependent Events Events that are NOT affected by previous or future events. Like tossing a coin, the probability is ALWAYS ½ no matter how many times you have already tossed heads Events that are affected by previous events what s the probability that the 3 rd card will be an Ace. This is dependent on the events before it. Just as with simple events, you determine the probability of compound events by finding all of the possible outcomes and the number of ways the given event can occur. Instead of P(A), however, you will probably have something like P(A,B) which would mean Probability of A then B see, two events! Check out these scenarios and classify them as compound or simple probability problems. Also state whether they are independent or dependent events. Justify each of your solutions: You are about to attack a bad guy in a role playing game. You will throw two dice, one numbered 1 to 10 and the other with the letters A through G. What is the probability that you will roll a 6 and a D? What are the odds that you would reach into your sock drawer and pull out a pair of orange socks if you have 3 red pair, 10 white pair, and 4 orange pair? A shuffled deck of cards is placed facedown on the table. It contains 7 hearts, 3 diamonds, 6 clubs and 5 spades. What is the probability that the top two cards are one of the hearts followed by one of the spades? Elizabeth wrote a computer program that generates two random numbers between 1 and 12. When she runs it, what is the probability that the first value will be more than 3 and the second will be less than 3? 1
4 2. Using organized Lists (7SP8) One strategy for solving probability problems that involve compound events is the use of an organized list. In an organized list, you simply make a list of all of the possible outcomes. Keeping it organized, however, it key or you are likely to miss one of the outcomes! Example: Your 3 friends, Allison, Bobby, and Cam are running a race. What is the probability that they will finish in alphabetical order? P(A, B, C) 1 st : figure out all of the possibilities (the solution set?) (A, B, C) (A, C, B) (B, A, C) (B, C, A) (C, B, A) (C, A, B) What makes this list organized?! 2 nd : How many meet the criteria (alphabetical order) only 1! 3 rd : Set up the fraction as 1/6 or 17%. Now try solving the following probability problems using an organized list: 1. In Clarajean's closet are four pairs of pants (black, white, grey, and brown), and five different shirts (blue, white, red, yellow, and purple). What is the likelihood that she would randomly draw out the same color of pants and shirt? 2
5 2. You are about to attack a bad guy in a role playing game. You will throw two dice, one numbered 1 to 10 and the other with the letters A through G. What is the probability that you will roll a 6 and a D? 3. A shuffled deck of cards is placed facedown on the table. It contains 7 hearts, 3 diamonds, 6 clubs and 5 spades. What is the probability that the top two cards are one of the hearts followed by one of the spades? 3
6 4. Elizabeth wrote a computer program that generates two random numbers between 1 and 12. When she runs it, what is the probability that the first value will be more than 3 and the second will be less than 3? 5. Above we determined that this scenario is NOT a compound event: What are the odds that you would reach into your sock drawer and pull out a pair of orange socks if you have 3 red pair, 10 white pair, and 4 orange pair? What could we do to the scenario to turn it into a compound event? 4
7 3. Using tables (7SP8) Another method of solving compound probability problems is with tables. You have probably used a lot of tables in your math career usually with ratios and maybe even a little bit with algebra. Mathematicians like tables because they help them keep things ORGANIZED! And sometimes when you are dealing with a lot of information, all you need to do to start finding patterns is to keep it organized. Check out this example: When rolling two dice, what is the probability that the sum will be larger than 10? 4 P(>10)= 6 36 = 1 6 I know these problems look familiar, but we are going to try them out now with a table instead of a list. This will help us to determine which method works best for us and for each problem! 1. In Clarajean's closet are four pairs of pants (black, white, grey, and brown), and five different shirts (blue, white, red, yellow, and purple). What is the likelihood that she would randomly draw out the same color of pants and shirt? 5
8 2. You are about to attack a bad guy in a role playing game. You will throw two dice, one numbered 1 to 10 and the other with the letters A through G. What is the probability that you will roll a 6 and a D? 3. A shuffled deck of cards is placed facedown on the table. It contains 7 hearts, 3 diamonds, 6 clubs and 5 spades. What is the probability that the top two cards are one of the hearts followed by one of the spades? 6
9 4. Elizabeth wrote a computer program that generates two random numbers between 1 and 12. When she runs it, what is the probability that the first value will be more than 3 and the second will be less than 3? 7
10 4. Using tree diagrams (7SP8) An organized list can get a little confusing when you get too many options and arrangements. And a table works very well for some situations, but not very well for others. So when all else fails, hug a tree! Wait, that s not what I meant when all else fails, use a tree diagram! In this instance, there is a tool called a tree diagram that can help you! As I mentioned in the first page of this packet, that is my favorite type of diagram for solving these problems. I hope you will like it too! A fair coin is tossed 3 times, what is the possibility of getting at least one head. number of ways >1head can occur P(>1 heads)= Total number of outcomes By looking at the diagram we can see that there is at least one heads in 7 of the 8 outcomes. Therefore P(>1 heads)= In Clarajean's closet are four pairs of pants (black, white, grey, and brown), and five different shirts (blue, white, red, yellow, and purple). What is the likelihood that she would randomly draw out the same color of pants and shirt? 8
11 2. You are about to attack a bad guy in a role playing game. You will throw two dice, one numbered 1 to 10 and the other with the letters A through G. What is the probability that you will roll a 6 and a D? 3. A shuffled deck of cards is placed facedown on the table. It contains 7 hearts, 3 diamonds, 6 clubs and 5 spades. What is the probability that the top two cards are one of the hearts followed by one of the spades? 9
12 4. Elizabeth wrote a computer program that generates two random numbers between 1 and 12. When she runs it, what is the probability that the first value will be more than 3 and the second will be less than 3? 10
13 5. Choose your method (7SP8) Now that you have mastered the organized list, table, and tree diagram, we are going to work through a variety of probability problems. In each of these scenarios you can pick whichever tool works best for you to solve the problem. If you come up with a strategy that isn t any of the three we have practiced so far, AWESOME! You are becoming a true mathematician and looking for patterns around every corner Show your teacher what you have come up with. 1. How many ways can a red, blue, and green marble be pulled from a bag? 11
14 2. Rolling the Dice: A fair sixsided die is rolled twice. What is the theoretical probability that the first number that comes up is greater than or equal to the second number? 3. Bag of Sweets! Joe has a bag containing 8 red sweets, 9 yellow ones and 11 green. He takes out a sweet and eats it, then, he takes out a second sweet. What is the probability that both the sweets are red? 12
15 4. The Lottery: Kent is thinking of holding a minilottery to raise money. Kent will sell tickets like this for $1 each. Each player must put a cross through 2 numbers on the ticket and hand it in. At the end of the week Karl will draw out two balls from a bag. Every player who has chosen the same two numbers as shown on the balls will win a cash prize of $10. (a) How many ways are there of choosing two different numbers on the ticket? Show all your work. (b) Will the lottery be a good money raiser? Describe your reasoning. 13
16 6. Charity Game: Ann is in charge of a barrel game to raise money for charities. Each barrel contains an equal number of red, green, white and black balls. The balls are buried in sawdust so that you cannot see them before you pick one out. To play the game, you give Ann your 25, then you pick one ball from each barrel. You win $5 if all three balls are the same color. (a) Calculate the probability that you will win the $5 if you play once. (b) Do you think that the barrel game will raise money for the local charities? Show your calculations (c) Ann wants to change the game so as to increase the amount of money it makes for the charities. Describe two different kinds of change that she could make to the Lucky Dip and find how much is likely to be raised for the charities after each change. Show all your calculations. 14
17 7. Computer Fight: Two teachers are fighting to use the computers. They play a dice game to determine which class will get to use the computers. If the die lands on an even number, your math teacher earns a point. If the die lands on an odd number, your English teacher, they earns a point. The first person to earn 5 points, wins the game and gets to use the computers. Currently your math teacher has 4 points and your English teacher has 2 points. What is the probability that your math teacher will win the game? What is the probability that your English teacher will win the game? 15
18 8. You Decide! Examine the tree diagram to the right. Come up with at least 3 questions that you could answer using this tree diagram. 16
19 9. Fair Game? James and Sam are playing a game with a coin and a dice labeled 16. They take turns tossing the coin and the number cube then they figure out the score If the coin lands on heads, the score is twice the number on the number cube. If the coin lands on tails, the score is two more than the number on the number cube. Complete this table of possible scores If the score is a prime number, James moves 2 squares on the board. If it s not, Sam moves one square on the board. What is the probability of getting a score that is a prime number? James and Sam play the game where there are 12 trials. How many squares would you expect James to move? How many squares would you expect Sam to move? Is the game fair?! 17
20 6. Using simulation (7SP8) The final lesson in probability here is simulation. In simulation, you will design and use a simulation to generate frequencies for compound events. A simulation is when you do something that represents a real life experiment without actually doing the experiment. For example, if 1/3 of the people in the city you live in have been to Mexico, you might want to ask some of them if they have been to Mexico to see how close your result is to the actual number. Instead of going and asking some people, you could take a dice and roll it once for every person you want to ask. You can say that every time you roll a 1 or 2, it represents someone who has been to Mexico, and every time you roll a 3, 4, 5, or 6, it represents someone who has not. It is easier than actually asking people, and it is a good simulation because you have the same chance of picking someone who has been to Mexico as you have of rolling a 1 or 2 on the dice. 1. Suppose each box of a popular brand of cereal contains a pen as a prize. The pens come in four colors, blue, red, green and yellow. Each color of pen is equally likely to appear in any box of cereal. Design and carry out a simulation to help you answer each of the following questions. a. What is the probability of having to buy at least five boxes of cereal to get a blue pen? What is the mean (average) number of boxes you would have to buy to get a blue pen if you repeated the process many times? b. What is the probability of having to buy at least ten boxes of cereal to get a full set of pens (all four colors)? What is the mean (average) number of boxes you would have to buy to get a full set of pens if you repeated the process many times? 18
21 2. Blood Type Simulation: Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 3. River Flooding: Suppose, over many years of records, a river generates a spring flood about 40% of the time. Based on these records, what is the chance that it will flood for at least three years in a row sometime during the next five years? 19
22 Probability Game MiniProject Project Description You and a partner will be responsible for interpreting and recreating a game related to probability. Contestants should be able to play the game and you the host should be able to explain the rules, strategies, and probability of the game. Project Requirements INSTRUCTION MANUAL/POSTER o o o Instructions on how to play the game At least two mathematical models that explain the outcomes of the game An explanation of the most effective strategy for winning the game GAME BOARD/SET o Materials needed to play the game TEAM WORK o Respectfully and equally share work load 20
Use this information to answer the following questions.
1 Lisa drew a token out of the bag, recorded the result, and then put the token back into the bag. She did this 30 times and recorded the results in a bar graph. Use this information to answer the following
More informationBasic Probability Ideas. Experiment  a situation involving chance or probability that leads to results called outcomes.
Basic Probability Ideas Experiment  a situation involving chance or probability that leads to results called outcomes. Random Experiment the process of observing the outcome of a chance event Simulation
More informationGrade 8 Math Assignment: Probability
Grade 8 Math Assignment: Probability Part 1: Rock, Paper, Scissors  The Study of Chance Purpose An introduction of the basic information on probability and statistics Materials: Two sets of hands Paper
More informationChapter 10 Practice Test Probability
Name: Class: Date: ID: A Chapter 0 Practice Test Probability Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the likelihood of the event given its
More informationThis Probability Packet Belongs to:
This Probability Packet Belongs to: 1 2 Station #1: M & M s 1. What is the sample space of your bag of M&M s? 2. Find the theoretical probability of the M&M s in your bag. Then, place the candy back into
More informationMATH STUDENT BOOK. 7th Grade Unit 6
MATH STUDENT BOOK 7th Grade Unit 6 Unit 6 Probability and Graphing Math 706 Probability and Graphing Introduction 3 1. Probability 5 Theoretical Probability 5 Experimental Probability 13 Sample Space 20
More informationMaking Predictions with Theoretical Probability. ESSENTIAL QUESTION How do you make predictions using theoretical probability?
L E S S O N 13.3 Making Predictions with Theoretical Probability 7.SP.3.6 predict the approximate relative frequency given the probability. Also 7.SP.3.7a ESSENTIAL QUESTION How do you make predictions
More informationFair Game Review. Chapter 9. Simplify the fraction
Name Date Chapter 9 Simplify the fraction. 1. 10 12 Fair Game Review 2. 36 72 3. 14 28 4. 18 26 5. 32 48 6. 65 91 7. There are 90 students involved in the mentoring program. Of these students, 60 are girls.
More informationPart 1: I can express probability as a fraction, decimal, and percent
Name: Pattern: Part 1: I can express probability as a fraction, decimal, and percent For #1 to #4, state the probability of each outcome. Write each answer as a) a fraction b) a decimal c) a percent Example:
More informationA. 15 B. 24 C. 45 D. 54
A spinner is divided into 8 equal sections. Lara spins the spinner 120 times. It lands on purple 30 times. How many more times does Lara need to spin the spinner and have it land on purple for the relative
More informationUnit 6: Probability Summative Assessment. 2. The probability of a given event can be represented as a ratio between what two numbers?
Math 7 Unit 6: Probability Summative Assessment Name Date Knowledge and Understanding 1. Explain the difference between theoretical and experimental probability. 2. The probability of a given event can
More informationUnit 7 Central Tendency and Probability
Name: Block: 7.1 Central Tendency 7.2 Introduction to Probability 7.3 Independent Events 7.4 Dependent Events 7.1 Central Tendency A central tendency is a central or value in a data set. We will look at
More informationUnit 11 Probability. Round 1 Round 2 Round 3 Round 4
Study Notes 11.1 Intro to Probability Unit 11 Probability Many events can t be predicted with total certainty. The best thing we can do is say how likely they are to happen, using the idea of probability.
More informationLesson 3: Chance Experiments with Equally Likely Outcomes
Lesson : Chance Experiments with Equally Likely Outcomes Classwork Example 1 Jamal, a 7 th grader, wants to design a game that involves tossing paper cups. Jamal tosses a paper cup five times and records
More informationMath 1313 Section 6.2 Definition of Probability
Math 1313 Section 6.2 Definition of Probability Probability is a measure of the likelihood that an event occurs. For example, if there is a 20% chance of rain tomorrow, that means that the probability
More information1. Theoretical probability is what should happen (based on math), while probability is what actually happens.
Name: Date: / / QUIZ DAY! FillintheBlanks: 1. Theoretical probability is what should happen (based on math), while probability is what actually happens. 2. As the number of trials increase, the experimental
More informationConditional Probability Worksheet
Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 36, compute the conditional probabilities P( AB) and P( B A ) 3. P A = 0.7, P B = 0.4, P A B = 0.25 4. P A = 0.45, P B = 0.8, P A
More informationMaking Predictions with Theoretical Probability
? LESSON 6.3 Making Predictions with Theoretical Probability ESSENTIAL QUESTION Proportionality 7.6.H Solve problems using qualitative and quantitative predictions and comparisons from simple experiments.
More informationSection 7.3 and 7.4 Probability of Independent Events
Section 7.3 and 7.4 Probability of Independent Events Grade 7 Review Two or more events are independent when one event does not affect the outcome of the other event(s). For example, flipping a coin and
More informationFoundations to Algebra In Class: Investigating Probability
Foundations to Algebra In Class: Investigating Probability Name Date How can I use probability to make predictions? Have you ever tried to predict which football team will win a big game? If so, you probably
More informationConditional Probability Worksheet
Conditional Probability Worksheet EXAMPLE 4. Drug Testing and Conditional Probability Suppose that a company claims it has a test that is 95% effective in determining whether an athlete is using a steroid.
More informationName. Is the game fair or not? Prove your answer with math. If the game is fair, play it 36 times and record the results.
Homework 5.1C You must complete table. Use math to decide if the game is fair or not. If Period the game is not fair, change the point system to make it fair. Game 1 Circle one: Fair or Not 2 six sided
More informationSTANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving.
Worksheet 4 th Topic : PROBABILITY TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving. BASIC COMPETENCY:
More informationProbability Essential Math 12 Mr. Morin
Probability Essential Math 12 Mr. Morin Name: Slot: Introduction Probability and Odds Single Event Probability and Odds Two and Multiple Event Experimental and Theoretical Probability Expected Value (Expected
More informationLesson 15.5: Independent and Dependent Events
Lesson 15.5: Independent and Dependent Events Sep 26 10:07 PM 1 Work with a partner. You have three marbles in a bag. There are two green marbles and one purple marble. Randomly draw a marble from the
More informationNAME DATE PERIOD. Study Guide and Intervention
91 Section Title The probability of a simple event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. Outcomes occur at random if each outcome occurs by chance.
More informationEssential Question How can you list the possible outcomes in the sample space of an experiment?
. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G..B Sample Spaces and Probability Essential Question How can you list the possible outcomes in the sample space of an experiment? The sample space of an experiment
More informationMath 7 Notes  Unit 7B (Chapter 11) Probability
Math 7 Notes  Unit 7B (Chapter 11) Probability Probability Syllabus Objective: (7.2)The student will determine the theoretical probability of an event. Syllabus Objective: (7.4)The student will compare
More informationFind the probability of an event by using the definition of probability
LESSON 101 Probability Lesson Objectives Find the probability of an event by using the definition of probability Vocabulary experiment (p. 522) trial (p. 522) outcome (p. 522) sample space (p. 522) event
More informationProbability. Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible
Probability Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible Impossible In summer, it doesn t rain much in Cape Town, so on a chosen
More informationPractice Ace Problems
Unit 6: Moving Straight Ahead Investigation 2: Experimental and Theoretical Probability Practice Ace Problems Directions: Please complete the necessary problems to earn a maximum of 12 points according
More informationInstructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include your name and student ID.
Math 3201 Unit 3 Probability Test 1 Unit Test Name: Part 1 Selected Response: Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include
More informationMost of the time we deal with theoretical probability. Experimental probability uses actual data that has been collected.
AFM Unit 7 Day 3 Notes Theoretical vs. Experimental Probability Name Date Definitions: Experiment: process that gives a definite result Outcomes: results Sample space: set of all possible outcomes Event:
More informationLesson 3 Dependent and Independent Events
Lesson 3 Dependent and Independent Events When working with 2 separate events, we must first consider if the first event affects the second event. Situation 1 Situation 2 Drawing two cards from a deck
More informationPROBABILITY. 1. Introduction. Candidates should able to:
PROBABILITY Candidates should able to: evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g for the total score when two fair dice are thrown), or by calculation
More informationLC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following.
A Ryan LC OL Probability ARNMaths.weebly.com Learning Outcomes As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. Counting List outcomes of an experiment Apply
More informationDate Learning Target/s Classwork Homework SelfAssess Your Learning. Pg. 23: WDYE 2.3: Designing a Fair Game
What Do You Expect: Probability and Expected Value Name: Per: Investigation 2: Experimental and Theoretical Probability Date Learning Target/s Classwork Homework SelfAssess Your Learning Mon, Feb. 29
More informationProbability of Independent and Dependent Events
706 Practice A Probability of In and ependent Events ecide whether each set of events is or. Explain your answer.. A student spins a spinner and rolls a number cube.. A student picks a raffle ticket from
More informationIndependent Events B R Y
. Independent Events Lesson Objectives Understand independent events. Use the multiplication rule and the addition rule of probability to solve problems with independent events. Vocabulary independent
More informationCounting Methods and Probability
CHAPTER Counting Methods and Probability Many good basketball players can make 90% of their free throws. However, the likelihood of a player making several free throws in a row will be less than 90%. You
More informationUnit 6: What Do You Expect? Investigation 2: Experimental and Theoretical Probability
Unit 6: What Do You Expect? Investigation 2: Experimental and Theoretical Probability Lesson Practice Problems Lesson 1: Predicting to Win (Finding Theoretical Probabilities) 13 Lesson 2: Choosing Marbles
More informationKey Concepts. Theoretical Probability. Terminology. Lesson 111
Key Concepts Theoretical Probability Lesson  Objective Teach students the terminology used in probability theory, and how to make calculations pertaining to experiments where all outcomes are equally
More informationIntermediate Math Circles November 1, 2017 Probability I
Intermediate Math Circles November 1, 2017 Probability I Probability is the study of uncertain events or outcomes. Games of chance that involve rolling dice or dealing cards are one obvious area of application.
More informationCCM6+7+ Unit 11 ~ Page 1. Name Teacher: Townsend ESTIMATED ASSESSMENT DATES:
CCM6+7+ Unit 11 ~ Page 1 CCM6+7+ UNIT 11 PROBABILITY Name Teacher: Townsend ESTIMATED ASSESSMENT DATES: Unit 11 Vocabulary List 2 Simple Event Probability 37 Expected Outcomes Making Predictions 89 Theoretical
More informationPROBABILITY. Example 1 The probability of choosing a heart from a deck of cards is given by
Classical Definition of Probability PROBABILITY Probability is the measure of how likely an event is. An experiment is a situation involving chance or probability that leads to results called outcomes.
More informationFunctional Skills Mathematics
Functional Skills Mathematics Level Learning Resource Probability D/L. Contents Independent Events D/L. Page  Combined Events D/L. Page  9 West Nottinghamshire College D/L. Information Independent Events
More informationName Date Class. 2. dime. 3. nickel. 6. randomly drawing 1 of the 4 S s from a bag of 100 Scrabble tiles
Name Date Class Practice A Tina has 3 quarters, 1 dime, and 6 nickels in her pocket. Find the probability of randomly drawing each of the following coins. Write your answer as a fraction, as a decimal,
More informationCompound Events: Making an Organized List
136 8 7.SP.6 7.SP.8a 7.SP.8b Objective Common Core State Standards Compound Events: Making an Organized List Experience with experiments helps students build on their intuitive sense about probability.
More informationMath 7 Notes  Unit 11 Probability
Math 7 Notes  Unit 11 Probability Probability Syllabus Objective: (7.2)The student will determine the theoretical probability of an event. Syllabus Objective: (7.4)The student will compare theoretical
More informationLesson 16.1 Assignment
Lesson 16.1 Assignment Name Date Rolling, Rolling, Rolling... Defining and Representing Probability 1. Rasheed is getting dressed in the dark. He reaches into his sock drawer to get a pair of socks. He
More informationName: Class: Date: ID: A
Class: Date: Chapter 0 review. A lunch menu consists of different kinds of sandwiches, different kinds of soup, and 6 different drinks. How many choices are there for ordering a sandwich, a bowl of soup,
More information#2. A coin is tossed 40 times and lands on heads 21 times. What is the experimental probability of the coin landing on tails?
1 PreAP Geometry Chapter 14 Test Review Standards/Goals: A.1.f.: I can find the probability of a simple event. F.1.c.: I can use area to solve problems involving geometric probability. S.CP.1: I can define
More informationProbability. March 06, J. Boulton MDM 4U1. P(A) = n(a) n(s) Introductory Probability
Most people think they understand odds and probability. Do you? Decision 1: Pick a card Decision 2: Switch or don't Outcomes: Make a tree diagram Do you think you understand probability? Probability Write
More informationProbability Assignment
Name Probability Assignment Student # Hr 1. An experiment consists of spinning the spinner one time. a. How many possible outcomes are there? b. List the sample space for the experiment. c. Determine the
More informationProbability. Probabilty Impossibe Unlikely Equally Likely Likely Certain
PROBABILITY Probability The likelihood or chance of an event occurring If an event is IMPOSSIBLE its probability is ZERO If an event is CERTAIN its probability is ONE So all probabilities lie between 0
More informationCompound Events. Identify events as simple or compound.
11.1 Compound Events Lesson Objectives Understand compound events. Represent compound events. Vocabulary compound event possibility diagram simple event tree diagram Understand Compound Events. A compound
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More 9.9.3 Practice Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. ) In how many ways can you answer the questions on
More informationSECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability
SECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability Name Period Write all probabilities as fractions in reduced form! Use the given information to complete problems 13. Five students have the
More informationMEP Practice Book SA5
5 Probability 5.1 Probabilities MEP Practice Book SA5 1. Describe the probability of the following events happening, using the terms Certain Very likely Possible Very unlikely Impossible (d) (e) (f) (g)
More information1. Decide whether the possible resulting events are equally likely. Explain. Possible resulting events
Applications. Decide whether the possible resulting events are equally likely. Explain. Action Possible resulting events a. You roll a number You roll an even number, or you roll an cube. odd number. b.
More informationName: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11
Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value
More information2. A bubblegum machine contains 25 gumballs. There are 12 green, 6 purple, 2 orange, and 5 yellow gumballs.
A C E Applications Connections Extensions Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability
More information4.1 Sample Spaces and Events
4.1 Sample Spaces and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment is called an
More information4.2.4 What if both events happen?
4.2.4 What if both events happen? Unions, Intersections, and Complements In the mid 1600 s, a French nobleman, the Chevalier de Mere, was wondering why he was losing money on a bet that he thought was
More informationALL FRACTIONS SHOULD BE IN SIMPLEST TERMS
Math 7 Probability Test Review Name: Date Hour Directions: Read each question carefully. Answer each question completely. ALL FRACTIONS SHOULD BE IN SIMPLEST TERMS! Show all your work for full credit!
More informationA 20% B 25% C 50% D 80% 2. Which spinner has a greater likelihood of landing on 5 rather than 3?
1. At a middle school, 1 of the students have a cell phone. If a student is chosen at 5 random, what is the probability the student does not have a cell phone? A 20% B 25% C 50% D 80% 2. Which spinner
More informationGrade 6 Math Circles Fall Oct 14/15 Probability
1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2014  Oct 14/15 Probability Probability is the likelihood of an event occurring.
More informationout one marble and then a second marble without replacing the first. What is the probability that both marbles will be white?
Example: Leah places four white marbles and two black marbles in a bag She plans to draw out one marble and then a second marble without replacing the first What is the probability that both marbles will
More information104 Theoretical Probability
Problem of the Day A spinner is divided into 4 different colored sections. It is designed so that the probability of spinning red is twice the probability of spinning green, the probability of spinning
More informationProbability WarmUp 2
Probability WarmUp 2 Directions Solve to the best of your ability. (1) Write out the sample space (all possible outcomes) for the following situation: A dice is rolled and then a color is chosen, blue
More informationUnit 1 Day 1: Sample Spaces and Subsets. Define: Sample Space. Define: Intersection of two sets (A B) Define: Union of two sets (A B)
Unit 1 Day 1: Sample Spaces and Subsets Students will be able to (SWBAT) describe events as subsets of sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,
More informationSection A Calculating Probabilities & Listing Outcomes Grade F D
Name: Teacher Assessment Section A Calculating Probabilities & Listing Outcomes Grade F D 1. A fair ordinary sixsided dice is thrown once. The boxes show some of the possible outcomes. Draw a line from
More informationBell Work. WarmUp Exercises. Two sixsided dice are rolled. Find the probability of each sum or 7
WarmUp Exercises Two sixsided dice are rolled. Find the probability of each sum. 1. 7 Bell Work 2. 5 or 7 3. You toss a coin 3 times. What is the probability of getting 3 heads? WarmUp Notes Exercises
More informationWhen a number cube is rolled once, the possible numbers that could show face up are
C3 Chapter 12 Understanding Probability Essential question: How can you describe the likelihood of an event? Example 1 Likelihood of an Event When a number cube is rolled once, the possible numbers that
More informationDate. Probability. Chapter
Date Probability Contests, lotteries, and games offer the chance to win just about anything. You can win a cup of coffee. Even better, you can win cars, houses, vacations, or millions of dollars. Games
More informationPRE TEST. Math in a Cultural Context*
P grade PRE TEST Salmon Fishing: Investigations into A 6P th module in the Math in a Cultural Context* UNIVERSITY OF ALASKA FAIRBANKS Student Name: Grade: Teacher: School: Location of School: Date: *This
More informationCHAPTER 9  COUNTING PRINCIPLES AND PROBABILITY
CHAPTER 9  COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many realworld fields, such as insurance, medical research, law enforcement, and political science. Objectives:
More information(a) Suppose you flip a coin and roll a die. Are the events obtain a head and roll a 5 dependent or independent events?
Unit 6 Probability Name: Date: Hour: Multiplication Rule of Probability By the end of this lesson, you will be able to Understand Independence Use the Multiplication Rule for independent events Independent
More informationApplications. 28 How Likely Is It? P(green) = 7 P(yellow) = 7 P(red) = 7. P(green) = 7 P(purple) = 7 P(orange) = 7 P(yellow) = 7
Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability that you will choose each color. P(green)
More informationProbability Test Review Math 2. a. What is? b. What is? c. ( ) d. ( )
Probability Test Review Math 2 Name 1. Use the following venn diagram to answer the question: Event A: Odd Numbers Event B: Numbers greater than 10 a. What is? b. What is? c. ( ) d. ( ) 2. In Jason's homeroom
More informationProbability Paradoxes
Probability Paradoxes Washington University Math Circle February 20, 2011 1 Introduction We re all familiar with the idea of probability, even if we haven t studied it. That is what makes probability so
More informationUNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet
Name Period Date UNIT 5: RATIO, PROPORTION, AND PERCENT WEEK 20: Student Packet 20.1 Solving Proportions 1 Add, subtract, multiply, and divide rational numbers. Use rates and proportions to solve problems.
More informationHere are two situations involving chance:
Obstacle Courses 1. Introduction. Here are two situations involving chance: (i) Someone rolls a die three times. (People usually roll dice in pairs, so dice is more common than die, the singular form.)
More informationChance and Probability
G Student Book Name Series G Contents Topic Chance and probability (pp. ) probability scale using samples to predict probability tree diagrams chance experiments using tables location, location apply lucky
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
6. Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the probability. ) A bag contains red marbles, blue marbles, and 8
More informationFinite Mathematics MAT 141: Chapter 8 Notes
Finite Mathematics MAT 4: Chapter 8 Notes Counting Principles; More David J. Gisch The Multiplication Principle; Permutations Multiplication Principle Multiplication Principle You can think of the multiplication
More informationAlgebra II Chapter 12 Test Review
Sections: Counting Principle Permutations Combinations Probability Name Choose the letter of the term that best matches each statement or phrase. 1. An illustration used to show the total number of A.
More informationMEP Practice Book ES5. 1. A coin is tossed, and a die is thrown. List all the possible outcomes.
5 Probability MEP Practice Book ES5 5. Outcome of Two Events 1. A coin is tossed, and a die is thrown. List all the possible outcomes. 2. A die is thrown twice. Copy the diagram below which shows all the
More informationPRE TEST KEY. Math in a Cultural Context*
PRE TEST KEY Salmon Fishing: Investigations into A 6 th grade module in the Math in a Cultural Context* UNIVERSITY OF ALASKA FAIRBANKS Student Name: PRE TEST KEY Grade: Teacher: School: Location of School:
More information4.3 Rules of Probability
4.3 Rules of Probability If a probability distribution is not uniform, to find the probability of a given event, add up the probabilities of all the individual outcomes that make up the event. Example:
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Study Guide for Test III (MATH 1630) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the number of subsets of the set. 1) {x x is an even
More informationSimulations. 1 The Concept
Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that can be
More informationSection Theoretical and Experimental Probability...Wks 3
Name: Class: Date: Section 6.8......Theoretical and Experimental Probability...Wks 3. Eight balls numbered from to 8 are placed in a basket. One ball is selected at random. Find the probability that it
More informationThe Teachers Circle Mar. 20, 2012 HOW TO GAMBLE IF YOU MUST (I ll bet you $5 that if you give me $10, I ll give you $20.)
The Teachers Circle Mar. 2, 22 HOW TO GAMBLE IF YOU MUST (I ll bet you $ that if you give me $, I ll give you $2.) Instructor: Paul Zeitz (zeitzp@usfca.edu) Basic Laws and Definitions of Probability If
More informationName: Probability, Part 1 March 4, 2013
1) Assuming all sections are equal in size, what is the probability of the spinner below stopping on a blue section? Write the probability as a fraction. 2) A bag contains 3 red marbles, 4 blue marbles,
More information* How many total outcomes are there if you are rolling two dice? (this is assuming that the dice are different, i.e. 1, 6 isn t the same as a 6, 1)
Compound probability and predictions Objective: Student will learn counting techniques * Go over HW Review counting tree All possible outcomes is called a sample space Go through Problem on P. 12, #2
More informationGeorgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Analytic Geometry Unit 7 PREASSESSMENT
PREASSESSMENT Name of Assessment Task: Compound Probability 1. State a definition for each of the following types of probability: A. Independent B. Dependent C. Conditional D. Mutually Exclusive E. Overlapping
More informationMiniUnit. Data & Statistics. Investigation 1: Correlations and Probability in Data
MiniUnit Data & Statistics Investigation 1: Correlations and Probability in Data I can Measure Variation in Data and Strength of Association in TwoVariable Data Lesson 3: Probability Probability is a
More informationWhat Do You Expect? Concepts
Important Concepts What Do You Expect? Concepts Examples Probability A number from 0 to 1 that describes the likelihood that an event will occur. Theoretical Probability A probability obtained by analyzing
More informationKS3 Levels 38. Unit 3 Probability. Homework Booklet. Complete this table indicating the homework you have been set and when it is due by.
Name: Maths Group: Tutor Set: Unit 3 Probability Homework Booklet KS3 Levels 38 Complete this table indicating the homework you have been set and when it is due by. Date Homework Due By Handed In Please
More information