Math 7 Notes  Unit 7B (Chapter 11) Probability


 Trevor Marsh
 3 years ago
 Views:
Transcription
1 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 theoretical and experimental probabilities of an event. Syllabus Objective: (7.5)The student will represent the probability of an event as a number between 0 and 1. Most of us would like to predict the future; just think of the possibilities if we could! Since we cannot, the best we can do is tell how likely something is to happen. It s helpful to know if something is impossible, likely, unlikely or certain to happen. People like to know if it is a sure thing, or a chance or it will never happen. It is more useful if you can use a number to describe the likelihood. Both probability and odds are ways to tell how likely it is that an event will or will not happen. Note to CCSD teachers: The textbook uses words or phrases to represent the probability of an event from impossible to certain. The CRT requires number values to represent probability (from 0 to 1). Probability is the measure of how likely an event is to occur. They are written as fractions or decimals from 0 to 1. Probability may be written as a percent, 0% to 100%. The higher the probability, the more likely an event is to happen. For instance, an event with a probability of 0 will never happen. If you have a probability of 100%, the event will always happen. An event with a probability of 1 2 or 50% has the same chance of happening as not happening. Example: How likely is it that a coin tossed will come up heads? This means that there is as likely a chance of heads as not heads. In other words, a probability of 1 or 0.5 or 50%. 2 Example: The weather report gives a 75% chance of rain for tomorrow. This means that there is a likely chance of rain (75%) and an unlikely chance of no rain (25%). In other words, the probability of rain is 3 or 0.75 or 75%. 4 Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 1 of 9
2 Outcomes are the possible results of an experiment. Example: Tossing a coin; the possible outcomes (results) are a head or a tail. Theoretical probability is based on knowing all the equally likely outcomes of an experiment, and it is defined as a ratio of the number of favorable outcomes to the number of possible outcomes. Mathematically, we write: probability = number of favorable outcomes number of possible outcomes or success probability = success + failure Example: Suppose you pick a marble from a hat that contains three red, two yellow and one blue marble. What is the probability you draw a yellow marble? P( yellow marbles ) = # of yellow marbles total number of marbles 2 1 P = or 6 3 The probability found in the above example is an example of theoretical probability. Experimental probability is based on repeated trials of an experiment. Example: In the last thirty days, there were 7 cloudy days. What is the experimental probability that tomorrow will be cloudy? 7 P( cloudy days ) = 30 Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 2 of 9
3 Odds Note to CCSD teachers: odds is not taught in the textbook; however, this concept is included in the CCSD benchmarks and Nevada Standards and will be tested on the CRT. Also, teachers should be aware that one can convert from odds to probability, and vice versa. For example, if the odds of winning a game is 2 3, then the probability of winning is 2. If the 5 probability of rain is 7 10, then the odds of rain is 7 3. Syllabus Objective: (7.3) The student will determine the odds of an event. Odds: the ratio of favorable outcomes to the number of unfavorable outcomes, when all outcomes are equally likely. Odds in favor = Odds against = Number of favorable outcomes Number of unfavorable outcomes Number of unfavorable outcomes Number of favorable outcomes Example: Suppose you pick a marble from a hat that contains three red, two yellow and one blue marble. What are the odds (in favor) you draw a yellow marble? 2 of yellow marbles 2 1 P = = = or 1:2 # of marbles not yellow 4 2 Example: If the probability of an event is 4, find the odds = 5, so the odds are. 5 Example: At a carnival ring toss game, an average of 3 people in 10 win a prize. Give the odds against winning the prize. number of favorable outcomes number of unfavorable outcomes = 7 3 Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 3 of 9
4 Tree Diagrams and The Fundamental Counting Principle One method students may use to determine the number of possible outcomes is to write an organized list. Example: Cassie has a blue sweater, a red sweater, and a purple sweater. She has a white shirt and a tan shirt. How many different ways can she wear a sweater and a shirt together? blue sweater white shirt or BW blue sweater tan shirt or BT red sweater white shirt or RW red sweater tan shirt or RT purple sweater white shirt or PW purple sweater tan shirt or PT 6 ways As more items are added, this method becomes cumbersome. A tree diagram makes it easier to see (count) the number of possible outcomes for experiments when the numbers are small and there are multiple events. To draw a tree diagram, you: 1) begin with a point; then you draw a segment for each outcome in the first event. 2) draw segments for subsequent outcomes based on the outcomes from the first event. Example: Draw a tree diagram to show the outcomes for flipping two coins. Start with a point. There are two outcomes for the first coin, a head (H) or a tail (T). Draw segments and label H and T. H T For either of the outcomes in the first flip, the second coin could be a head or a tail. So the tree diagram would look like this. Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 4 of 9
5 H T H T H T Now reading down the tree diagram, the possible outcomes are HH, HT, TH, or TT. There are 4 possible outcomes when flipping two coins. Extend the tree diagram for three coins. How many outcomes are there? Example: Draw a tree diagram to determine the number of different outfits that could be worn if you had two pairs of pants and three shirts. Starting with a point, you have 2 pairs of pants. For each pair of pants (P1 and P2), you have three shirts (S1, S2 and S3) to choose from. P1 P2 S1 S2 S3 S1 S2 S3 There are 6 possible outcomes: P1S1, P1S2, P1S3, P2S1, P2S2, and P2S3. Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 5 of 9
6 Fundamental Counting Principle Tree diagrams are useful to get a picture of what is occurring, but with a large number of events, the tree can get out of hand in a hurry. A quick way to determine the number of possible outcomes in a tree diagram is to multiply the number of outcomes in each event. With the first example using 2 coins, there are 2 outcomes when you flip the first coin and two outcomes when you flip the second coin. 2 2= 4. In the last example, we choose from 2 pairs of pants, then from three shirts. Notice the total number of outcomes we identified using the tree diagram was 6 and 2 3= 6. Those examples lead us to the following generalization: Fundamental Counting Principle: If one event can occur in m ways, and for each of these ways a second event can happen in n ways, then the number of ways that the two events can occur is m n. Example: How many possible outcomes are there if you roll two cubes with the numbers one through six written on each face? There are 6 outcomes on the first cube, 6 outcomes on the second cube, so using the Fundamental Counting Principal we have 6 6 = 36 outcomes. Example: How many possible outcomes are possible for tossing a coin and rolling a cube with the numbers one through six written on each face? There are two things that can happen when tossing a coin. There are six things that can happen when rolling the cube. Using the Fundamental Counting Principle, we have 2 6 = 12 outcomes. Example: How many possible answers are there to a 10 question TrueFalse test? Using Fundamental Counting Principal, = 2 = Let s extend this to finding the probability of compound events (an event made up of two or more separate events). If the occurrence of one event does not affect the probability of the other, the events are independent. If the occurrence of one event does have an effect on the probability that the second event will occur, the events are dependent. Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 6 of 9
7 Examples of independent and dependent events Example: A student rolls a number cube, then rolls a second time and records each result. These events are independent since the outcome of rolling one number cube does not affect the outcome of rolling the number cube the second time. Example: One student chooses a book off a library shelf. A second student then choses a different book off the same shelf from the remaining books. These events are dependent since the students must choose different books and the second student has fewer books to choose from. Example: A student rolls a number cube and then flips a coin. These events are independent since the rolling of a number cube does not affect the outcome of flipping a coin. Example: the first. A student draws an item from a bag, then draws a second item without replacing These events are dependent since the outcome of the first draw affects the outcome of the second draw (remember the second draw contains one less item than the first draw). Example: A student draws an item from a bag, replaces it, then draws a second item. These events are independent since the outcome of the first draw does not affect the outcome of the second draw Probability of Independent Events = P(A) P(B) Example: An experiment consists of flipping a coin 2 times. What is the probability of flipping heads both times? The flip of a coin does not affect the results of the other flips, so the flips are independent. For each flip, P(H) = So P(H, H) = or Example: You have 3 colors of tshirts (red, blue, green) 2 colors of shorts (white, black) from which to choose. What is the probability of randomly choosing a blue shirt with black pants? For the choice of shirt, P(T) = 1 3, for the shorts P(S) = ; So P(T, S) = or Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 7 of 9
8 Probability of Dependent Events P(A and B) = P(A) P(B after A) Example: Seven different books are on a shelf in the classroom. If Jewel chooses a book from the shelf to read, and then Cheryl chooses a book from the ones that remain, what is the probability of them choosing Book 1 and Book 2? P(Book 1) = 1 7. The P(Book 2) = 1 6. P(Book 1, then Book 2) 1 1 = Remember when Cheryl chooses a book there is one less book on the shelf. So 7 1 = 6 OnCore Examples 1. In a hat, you have index cards with the numbers 1 through 10 written on them. You pick one card at random, Order the events from least likely to happen to most likely to happen. You pick a number greater than 0. You pick an even number. You pick a number that is at least 2. You pick a number that is at most Determine whether each event below is impossible, unlikely, as likely as not, likely, or certain. Then tell whether the probability is 0, close to 0, 1, close to 1 or 1. 2 A. The probability of rolling a 5 on a number cube is 1. What is the probability of 6 not rolling a 5? B. Picking a number less than 15 from a jar with papers labeled from 1 to 12. C. Picking a number that is divisible by 5 from a jar with papers labeled from 1 to Describe an event that has a probability of 0% and an event that has a probability of 100%. Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 8 of 9
9 Applicable CCSS Example (Although technically it has not rolled out yet but a similar standard in NSS is still in place) Standard: 7.SP.5 DOK: 3 Difficulty: Medium Type: Extended Response Carl and Beneta are playing a game using this spinner. Carl will win the game on his next spin if the arrow lands on a section labeled 6, 7, or 8. Carl claims it is likely, but not certain, that he will win the game on his next spin. Explain why Carl s claim is not correct. Beneta will win the game on her next spin if the result of the spin satisfies event X. Beneta claims it is likely, but not certain, that she will win the game on her next spin. Describe an event X for which Beneta s claim is correct. Math 7, Unit 7B (Ch 11): Probability Holt: Chapter 11 Page 9 of 9
Math 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 informationMath 7, Unit 5: Probability  NOTES
Math 7, Unit 5: Probability  NOTES NVACS 7. SP.C.5  Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers
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 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 informationINDEPENDENT AND DEPENDENT EVENTS UNIT 6: PROBABILITY DAY 2
INDEPENDENT AND DEPENDENT EVENTS UNIT 6: PROBABILITY DAY 2 WARM UP Students in a mathematics class pick a card from a standard deck of 52 cards, record the suit, and return the card to the deck. The results
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 informationLesson Lesson 3.7 ~ Theoretical Probability
Theoretical Probability Lesson.7 EXPLORE! sum of two number cubes Step : Copy and complete the chart below. It shows the possible outcomes of one number cube across the top, and a second down the left
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 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 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 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 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 informationLesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes
NYS COMMON CORE MAEMAICS CURRICULUM 7 : Calculating Probabilities for Chance Experiments with Equally Likely Classwork Examples: heoretical Probability In a previous lesson, you saw that to find an estimate
More informationMATH STUDENT BOOK. 6th Grade Unit 7
MATH STUDENT BOOK 6th Grade Unit 7 Unit 7 Probability and Geometry MATH 607 Probability and Geometry. PROBABILITY 5 INTRODUCTION TO PROBABILITY 6 COMPLEMENTARY EVENTS SAMPLE SPACE 7 PROJECT: THEORETICAL
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 informationLesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes
Lesson : Calculating Probabilities for Chance Experiments with Equally Likely Outcomes Classwork Example : heoretical Probability In a previous lesson, you saw that to find an estimate of the probability
More informationProbability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College
Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical
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 informationCH 13. Probability and Data Analysis
11.1: Find Probabilities and Odds 11.2: Find Probabilities Using Permutations 11.3: Find Probabilities Using Combinations 11.4: Find Probabilities of Compound Events 11.5: Analyze Surveys and Samples 11.6:
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 informationLesson 1: Chance Experiments
Student Outcomes Students understand that a probability is a number between and that represents the likelihood that an event will occur. Students interpret a probability as the proportion of the time that
More informationCOMPOUND EVENTS. Judo Math Inc.
COMPOUND EVENTS Judo Math Inc. 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)
More informationName Date Class. Identify the sample space and the outcome shown for each experiment. 1. spinning a spinner
Name Date Class 0.5 Practice B Experimental Probability Identify the sample space and the outcome shown for each experiment.. spinning a spinner 2. tossing two coins Write impossible, unlikely, as likely
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 informationProbability of Independent and Dependent Events 106
* Probability of Independent and Dependent Events 106 Vocabulary Independent events the occurrence of one event has no effect on the probability that a second event will occur. Dependent events the
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 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 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 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 informationUse 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 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 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 informationMath 7 /Unit 5 Practice Test: Probability
Math 7 /Unit 5 Practice Test: Probability Name Date 1. Define probability. 2. Define experimental probability.. Define sample space for an experiment 4. What makes experimental probability different from
More informationTEKSING TOWARD STAAR MATHEMATICS GRADE 7. Projection Masters
TEKSING TOWARD STAAR MATHEMATICS GRADE 7 Projection Masters Six Weeks 1 Lesson 1 STAAR Category 1 Grade 7 Mathematics TEKS 7.2A Understanding Rational Numbers A group of items or numbers is called a set.
More informationProbability and the Monty Hall Problem Rong Huang January 10, 2016
Probability and the Monty Hall Problem Rong Huang January 10, 2016 Warmup: There is a sequence of number: 1, 2, 4, 8, 16, 32, 64, How does this sequence work? How do you get the next number from the previous
More informationProbability of Independent and Dependent Events. CCM2 Unit 6: Probability
Probability of Independent and Dependent Events CCM2 Unit 6: Probability Independent and Dependent Events Independent Events: two events are said to be independent when one event has no affect on the probability
More informationCompound Probability. A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events.
Probability 68B A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events. Independent Events are events in which the result of event
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 informationCommon Core Math Tutorial and Practice
Common Core Math Tutorial and Practice TABLE OF CONTENTS Chapter One Number and Numerical Operations Number Sense...4 Ratios, Proportions, and Percents...12 Comparing and Ordering...19 Equivalent Numbers,
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 informationWhat is the probability Jordan will pick a red marble out of the bag and land on the red section when spinning the spinner?
Name: Class: Date: Question #1 Jordan has a bag of marbles and a spinner. The bag of marbles has 10 marbles in it, 6 of which are red. The spinner is divided into 4 equal sections: blue, green, red, and
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 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 informationgreen, green, green, green, green The favorable outcomes of the event are blue and red.
5 Chapter Review Review Key Vocabulary experiment, p. 6 outcomes, p. 6 event, p. 6 favorable outcomes, p. 6 probability, p. 60 relative frequency, p. 6 Review Examples and Exercises experimental probability,
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 informationName: Unit 7 Study Guide 1. Use the spinner to name the color that fits each of the following statements.
1. Use the spinner to name the color that fits each of the following statements. green blue white white blue a. The spinner will land on this color about as often as it lands on white. b. The chance of
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 informationPractice 91. Probability
Practice 91 Probability You spin a spinner numbered 1 through 10. Each outcome is equally likely. Find the probabilities below as a fraction, decimal, and percent. 1. P(9) 2. P(even) 3. P(number 4. P(multiple
More informationWelcome! U4H2: Worksheet # s 27, 913, 16, 20. Updates: U4T is 12/12. Announcement: December 16 th is the last day I will accept late work.
Welcome! U4H2: Worksheet # s 27, 913, 16, 20 Updates: U4T is 12/12 Announcement: December 16 th is the last day I will accept late work. 1 Review U4H1 2 Theoretical Probability 3 Experimental Probability
More informationLesson 17.1 Assignment
Lesson 17.1 Assignment Name Date Is It Better to Guess? Using Models for Probability Charlie got a new board game. 1. The game came with the spinner shown. 6 7 9 2 3 4 a. List the sample space for using
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 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 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 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 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 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 informationNow let s figure the probability that Angelina picked a green marble if Marc did not replace his marble.
Find the probability of an event with or without replacement : The probability of an outcome of an event is the ratio of the number of ways that outcome can occur to the total number of different possible
More informationOrder the fractions from least to greatest. Use Benchmark Fractions to help you. First try to decide which is greater than ½ and which is less than ½
Outcome G Order the fractions from least to greatest 4 1 7 4 5 3 9 5 8 5 7 10 Use Benchmark Fractions to help you. First try to decide which is greater than ½ and which is less than ½ Likelihood Certain
More information3.6 Theoretical and Experimental Coin Tosses
wwwck12org Chapter 3 Introduction to Discrete Random Variables 36 Theoretical and Experimental Coin Tosses Here you ll simulate coin tosses using technology to calculate experimental probability Then you
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 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 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 informationCh Probability Outcomes & Trials
Learning Intentions: Ch. 10.2 Probability Outcomes & Trials Define the basic terms & concepts of probability. Find experimental probabilities. Calculate theoretical probabilities. Vocabulary: Trial: realworld
More informationWhat Do You Expect Unit (WDYE): Probability and Expected Value
Name: Per: What Do You Expect Unit (WDYE): Probability and Expected Value Investigations 1 & 2: A First Look at Chance and Experimental and Theoretical Probability Date Learning Target/s Classwork Homework
More informationProbability Rules. 2) The probability, P, of any event ranges from which of the following?
Name: WORKSHEET : Date: Answer the following questions. 1) Probability of event E occurring is... P(E) = Number of ways to get E/Total number of outcomes possible in S, the sample space....if. 2) The probability,
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 informationBellwork Write each fraction as a percent Evaluate P P C C 6
Bellwork 21915 Write each fraction as a percent. 1. 2. 3. 4. Evaluate. 5. 6 P 3 6. 5 P 2 7. 7 C 4 8. 8 C 6 1 Objectives Find the theoretical probability of an event. Find the experimental probability
More informationLearn to find the probability of independent and dependent events.
Learn to find the probability of independent and dependent events. Dependent Insert Lesson Events Title Here Vocabulary independent events dependent events Raji and Kara must each choose a topic from a
More informationDate Learning Target/s Classwork Homework SelfAssess Your Learning. Pg. 23: WDYE 3.1: Designing a Spinner. Pg. 56: WDYE 3.2: Making Decisions
What Do You Expect: Probability and Expected Value Name: Per: Investigation 3: Making Decisions and Investigation 4: Area Models Date Learning Target/s Classwork Homework SelfAssess Your Learning Fri,
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 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 informationMATH7 SOL Review 7.9 and Probability and FCP Exam not valid for Paper Pencil Test Sessions
MATH7 SOL Review 7.9 and 7.0  Probability and FCP Exam not valid for Paper Pencil Test Sessions [Exam ID:LV0BM Directions: Click on a box to choose the number you want to select. You must select all
More informationTake a Chance on Probability. Probability and Statistics is one of the strands tested on the California Standards Test.
Grades 4 Probability and tatistics is one of the strands tested on the California tandards Test. Probability is introduced in rd grade. Many students do not work on probability concepts in 5 th grade.
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 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 informationProbability and Statistics 15% of EOC
MGSE912.S.CP.1 1. Which of the following is true for A U B A: 2, 4, 6, 8 B: 5, 6, 7, 8, 9, 10 A. 6, 8 B. 2, 4, 6, 8 C. 2, 4, 5, 6, 6, 7, 8, 8, 9, 10 D. 2, 4, 5, 6, 7, 8, 9, 10 2. This Venn diagram shows
More informationReview. Natural Numbers: Whole Numbers: Integers: Rational Numbers: Outline Sec Comparing Rational Numbers
FOUNDATIONS Outline Sec. 31 Gallo Name: Date: Review Natural Numbers: Whole Numbers: Integers: Rational Numbers: Comparing Rational Numbers Fractions: A way of representing a division of a whole into
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 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 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 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 informationProbability. facts mental math. problem solving. Power Up F
LESSON 7 Probability Power Up facts mental math Power Up F a. Estimation: The width of the paperback book is inches. Round this measurement to the nearest inch. in. b. Geometry: An octagon has how many
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 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 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 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 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 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 informationAlgebra I Notes Unit One: Real Number System
Syllabus Objectives: 1.1 The student will organize statistical data through the use of matrices (with and without technology). 1.2 The student will perform addition, subtraction, and scalar multiplication
More informationName Class Date. Introducing Probability Distributions
Name Class Date Binomial Distributions Extension: Distributions Essential question: What is a probability distribution and how is it displayed? 86 CC.9 2.S.MD.5(+) ENGAGE Introducing Distributions Video
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 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 informationFAVORITE MEALS NUMBER OF PEOPLE Hamburger and French fries 17 Spaghetti 8 Chili 12 Vegetarian delight 3
Probability 1. Destiny surveyed customers in a restaurant to find out their favorite meal. The results of the survey are shown in the table. One person in the restaurant will be picked at random. Based
More informationIndependent and Mutually Exclusive Events
Independent and Mutually Exclusive Events By: OpenStaxCollege Independent and mutually exclusive do not mean the same thing. Independent Events Two events are independent if the following are true: P(A
More informationProbability: introduction
May 6, 2009 Probability: introduction page 1 Probability: introduction Probability is the part of mathematics that deals with the chance or the likelihood that things will happen The probability of an
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 information1. a. Miki tosses a coin 50 times, and the coin shows heads 28 times. What fraction of the 50 tosses is heads? What percent is this?
A C E Applications Connections Extensions Applications 1. a. Miki tosses a coin 50 times, and the coin shows heads 28 times. What fraction of the 50 tosses is heads? What percent is this? b. Suppose the
More informationBasic Probability. Let! = # 8 # < 13, # N ,., and / are the subsets of! such that  = multiples of four. = factors of 24 / = square numbers
Basic Probability Let! = # 8 # < 13, # N ,., and / are the subsets of! such that  = multiples of four. = factors of 24 / = square numbers (a) List the elements of!. (b) (i) Draw a Venn diagram to show
More information