Outcomes: The outcomes of this experiment are yellow, blue, red and green.


 Eleanor Dina Tucker
 3 years ago
 Views:
Transcription
1 (Adapted from 1. Sample Space The sample space of an experiment is the set of all possible outcomes of that experiment. The sum of the probabilities of the distinct outcomes within a sample space is 1. Ex 1: What is the probability of each outcome when a coin is tossed? Outcomes: The outcomes of this experiment are head and tail. P(Head) = 0.5 P(Tail) = 0.5 The events Head and Tail are mutually exclusive and exhaustive and thus they are complementary events. P(Head) + P(Tail) = 1 The sample space of Experiment 1 is: {head, tail} Ex 2: A spinner has 4 equal sectors coloured yellow, blue, green and red. What is the probability of landing on each colour after spinning this spinner? Outcomes: The outcomes of this experiment are yellow, blue, red and green. P(yellow) = 0.25 P(blue) = 0.25 P(red) = 0.25 P(green) = 0.25 The events yellow, blue, red and green are mutually exclusive and exhaustive and thus they are complementary events. P(Y) + P(B) + P(R) + P(G) = 1 The sample space of Experiment 2 is: {Yellow, Blue, Red, Green}
2 Exercises 1. What is the sample space for choosing an odd number from 1 to 11 at random? A: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 B: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} C: {1, 3, 5, 7, 9 11} 2. What is the sample space for choosing a prime number less than 15 at random? A: {2, 3, 5, 7, 11, 13, 15} B; {2, 3, 5, 7, 11, 13} C: {2, 3, 5, 7, 9, 11, 13} D: All of the above. 3. What is the sample space for choosing 1 jellybean at random from a jar containing 5 red, 7 blue and 2 green jellybeans? A: {5, 7, 2} B: {5 red, 7 blue, 2 green} C: {red, blue, green} 4. What is the sample space for choosing 1 letter at random from 5 vowels? A: {a, e, i, o, u} B: {v, o, w, e, l} C: {1, 2, 3, 4, 5} 5. What is the sample space for choosing 1 letter at random from the word DIVIDE? A: {d, i, v, i, d, e} B: {1, 2, 3, 4, 5, 6} C: {d, i, v, e}
3 2. Addition Rule for calculating probabilities To find the probability of event A or B, we must first determine whether the events are mutually exclusive or nonmutually exclusive. Then we can apply the appropriate Addition Rule: Addition Rule 1: When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event. P(A or B) = P(A) + P(B) Addition Rule 2: When two events, A and B, are nonmutually exclusive, there is some overlap between these events. The probability that A or B will occur is the sum of the probability of each event, minus the probability of the overlap. P(A or B) = P(A) + P(B)  P(A and B) Examples Ex 1: A single 6sided die is rolled. What is the probability of rolling a 2 or a 5? Probabilities: These events are mutually exclusive since they cannot occur at the same time. P(2 or 5) = P(2) + P(5) = 1/6 + 1/6 = 2/6 = 1/3 Ex 2: In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls achieved an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student? Probabilities: These events are NOT mutually exclusive since it is possible for a student, chosen randomly, to be a girl and an A student. P(girl or A) = P(girl) + P(A)  P(girl and A) = 13/30 + 9/305/30 = 17/30
4 Exercises 1. A day of the week is chosen at random. What is the probability of choosing a Monday or Tuesday? A: 1/7 B: 1/14 C: 2/7 2. In a pet store, there are 6 puppies, 9 kittens, 4 gerbils and 7 parakeets. If a pet is chosen at random, what is the probability of choosing a puppy or a parakeet? A: 15/26 B: 1/2 C: 11/26 3. The probability of a New York teenager owning a skateboard is 0.37, of owning a bicycle is 0.81 and of owning both is If a New York teenager is chosen at random, what is the probability that the teenager owns a skateboard or a bicycle? A: 1.18 B: 0.7 C: A number from 1 to 10 is chosen at random. What is the probability of choosing a 5 or an even number? A: 3/5 B: 1/2 C: 1/5 D: All of the above. 5. A single 6sided die is rolled. What is the probability of rolling a number greater than 3 or an even number? A: 1 B: 2/3 C: 5/6
5 3. Independent events Definition: Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Some examples of independent events are: 1. Landing on heads after tossing a coin AND rolling a 5 on a single 6sided die. 2. Choosing a marble from a jar AND landing on heads after tossing a coin. 3. Choosing a 3 from a deck of cards, replacing it, AND then choosing an ace as the second card. 4. Rolling a 4 on a single 6sided die, AND then rolling a 1 on a second roll of the die. To find the probability of two independent events that occur in sequence, find the probability of each event occurring separately, and then multiply the probabilities. This multiplication rule is defined symbolically below. Note that multiplication is represented by AND. Multiplication Rule 1: When two events, A and B, are independent, the probability of both occurring is: P(A and B) = P(A) x P(B) Examples Ex 1: A coin is tossed and a single 6sided die is rolled. Find the probability of tossing a head and rolling a 3 on the die. NB: These are independent events. Probabilities: P(head) = 1/2 ; P(3) = 1/6 P(head and 3) = P(head) x P(3) = 1/2 x 1/6 = 1/12 Multiplication Rule 1 can be extended to work for three or more independent events that occur in sequence as follows: Ex 2: A school survey found that 9 out of 10 students like pizza. If three students are chosen at random with replacement, what is the probability that all three students like pizza? Probabilities: P(student 1 likes pizza) = 9/10 P(student 2 likes pizza) = 9/10
6 P(student 3 likes pizza) = 9/10 P(student 1 and student 2 and student 3 like pizza) = 9/10 x 9/10 x 9/10 Exercises = 729/1000 = = 72.9% 1. Spin a spinner numbered 1 to 7, and toss a coin. What is the probability of getting an odd number on the spinner and a tail on the coin? A: 3/14 B: 2/7 C: 5/14 2. A jar contains 6 red balls, 3 green balls, 5 white balls and 7 yellow balls. Two balls are chosen from the jar, with replacement. What is the probability that both balls chosen are green? A: 6/441 B: 1/49 C: 2/49 D: None of the above 3. In Exercise 2 above, what is the probability of choosing a red and then a yellow ball? A: 2/21 B: 3/21 C: 13/63 D: All of the above. 4. Four cards are chosen from a standard deck of 52 playing cards with replacement. What is the probability of choosing 4 hearts in a row? A: 13/52 B: 1/16 C: 1/256
7 5. A nationwide survey showed that 65% of all children in the United States dislike eating vegetables. If 4 children are chosen at random, what is the probability that all 4 dislike eating vegetables? (Round your answer to the nearest percent.) A: 18% B: 260% C: 2% 4. Dependent events Definition: Two events are dependent if the outcome or occurrence of the first event A affects the outcome or occurrence of the second event B, so that the probability of event B is changed. This leads to the following concept: Definition: The conditional probability of an event B in relationship to an event A is the probability that event B occurs given that event A has already occurred. The notation for conditional probability is P(B A) [pronounced as The probability of event B given A ]. Multiplication Rule 2: When two events, A and B, are dependent, the probability of both occurring is: P(A and B) = P(A) x P(B A) Examples Ex 1: A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack? Probabilities: P(queen on first pick) = 4/52 P(jack on 2nd pick queen) = 4/51 P(queen and jack) = 4/52 x 4/51 = 16/2652 = 4/663 = 0.6%
8 Ex 2: Mr Moser, who has changed schools to teach at a coed school, needs two students to help him with a science demonstration for his class of 18 girls and 12 boys. He randomly chooses one student. He then chooses a second student from those still seated. What is the probability that both students chosen are girls? Probabilities: P(Girl 1 and Girl 2) = P(Girl 1) x P(Girl 2 Girl 1) = 18/30 x 17/29 = 306/870 = 51/145 = 35.2% Ex 3: Three cards are chosen at random from a deck of 52 cards without replacement. What is the probability of choosing 3 aces? Probabilities: P(3 aces) = 4/52 x 3/51 x 2/50 = 24/ = 1/5525 = 0.02% Exercises 1. Two cards are chosen at random from a deck of 52 cards without replacement. What is the probability of choosing two kings? A: 4/663 B: 1/221 C: 1/69 2. Two cards are chosen at random from a deck of 52 cards without replacement. What is the probability that the first card is a jack and the second card is a ten? A: 3/676 B: 1/169 C: 4/663
9 3. On a math test, 5 out of 20 students got an A. If three students are chosen at random without replacement, what is the probability that all three got an A on the test? A: 1/114 B: 25/1368 C: 3/ Three cards are chosen at random from a deck of 52 cards without replacement. What is the probability of choosing an ace, a king, and a queen in order? A: 1/2197 B: 8/5525 C: 8/ A school survey found that 7 out of 30 students walk to school. If four students are selected at random without replacement, what is the probability that all four walk to school? A: 343/93960 B: 1/783 C: 7/6750
Objectives. Determine whether events are independent or dependent. Find the probability of independent and dependent events.
Objectives Determine whether events are independent or dependent. Find the probability of independent and dependent events. independent events dependent events conditional probability Vocabulary Events
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 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 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 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 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 informationDefine and Diagram Outcomes (Subsets) of the Sample Space (Universal Set)
12.3 and 12.4 Notes Geometry 1 Diagramming the Sample Space using Venn Diagrams A sample space represents all things that could occur for a given event. In set theory language this would be known as the
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 informationthe total number of possible outcomes = 1 2 Example 2
6.2 Sets and Probability  A useful application of set theory is in an area of mathematics known as probability. Example 1 To determine which football team will kick off to begin the game, a coin is tossed
More informationProbability. Ms. Weinstein Probability & Statistics
Probability Ms. Weinstein Probability & Statistics Definitions Sample Space The sample space, S, of a random phenomenon is the set of all possible outcomes. Event An event is a set of outcomes of a random
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 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 informationProbability. Mutually Exclusive Events
Probability Mutually Exclusive Events Mutually Exclusive Outcomes Outcomes are mutually exclusive if they cannot happen at the same time. For example, when you toss a single coin either it will land on
More informationChapter 13 Test Review
1. The tree diagrams below show the sample space of choosing a cushion cover or a bedspread in silk or in cotton in red, orange, or green. Write the number of possible outcomes. A 6 B 10 C 12 D 4 Find
More informationName: Section: Date:
WORKSHEET 5: PROBABILITY Name: Section: Date: Answer the following problems and show computations on the blank spaces provided. 1. In a class there are 14 boys and 16 girls. What is the probability of
More informationUnit 9: Probability Assignments
Unit 9: Probability Assignments #1: Basic Probability In each of exercises 1 & 2, find the probability that the spinner shown would land on (a) red, (b) yellow, (c) blue. 1. 2. Y B B Y B R Y Y B R 3. Suppose
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 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 informationObjective: Determine empirical probability based on specific sample data. (AA21)
Do Now: What is an experiment? List some experiments. What types of things does one take a "chance" on? Mar 1 3:33 PM Date: Probability  Empirical  By Experiment Objective: Determine empirical probability
More informationObjectives To find probabilities of mutually exclusive and overlapping events To find probabilities of independent and dependent events
CC Probability of Compound Events Common Core State Standards MACCSCP Apply the Addition Rule, P(A or B) = P(A) + P(B)  P(A and B), and interpret the answer in terms of the model Also MACCSCP MP, MP,
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 informationCC13. Start with a plan. How many songs. are there MATHEMATICAL PRACTICES
CC Interactive Learning Solve It! PURPOSE To determine the probability of a compound event using simple probability PROCESS Students may use simple probability by determining the number of favorable outcomes
More informationClassical vs. Empirical Probability Activity
Name: Date: Hour : Classical vs. Empirical Probability Activity (100 Formative Points) For this activity, you will be taking part in 5 different probability experiments: Rolling dice, drawing cards, drawing
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 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 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 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 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 information7.1 Experiments, Sample Spaces, and Events
7.1 Experiments, 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
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 informationheads 1/2 1/6 roll a die sum on 2 dice 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 1, 2, 3, 4, 5, 6 heads tails 3/36 = 1/12 toss a coin trial: an occurrence
trial: an occurrence roll a die toss a coin sum on 2 dice sample space: all the things that could happen in each trial 1, 2, 3, 4, 5, 6 heads tails 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 example of an outcome:
More informationChapter 1  Set Theory
Midterm review Math 3201 Name: Chapter 1  Set Theory Part 1: Multiple Choice : 1) U = {hockey, basketball, golf, tennis, volleyball, soccer}. If B = {sports that use a ball}, which element would be in
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 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 informationWhat s the Probability I Can Draw That? Janet Tomlinson & Kelly Edenfield
What s the Probability I Can Draw That? Janet Tomlinson & Kelly Edenfield Engage Your Brain On your seat you should have found a list of 5 events and a number line on which to rate the probability of those
More informationRevision 6: Similar Triangles and Probability
Revision 6: Similar Triangles and Probability Name: lass: ate: Mark / 52 % 1) Find the missing length, x, in triangle below 5 cm 6 cm 15 cm 21 cm F 2) Find the missing length, x, in triangle F below 5
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 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 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 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 information05 Adding Probabilities. 1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins.
1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins. d. a. Copy the table and add a column to show the experimental probability of the spinner landing on
More informationTopic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes
Worksheet 6 th Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of
More informationProbability. Chapter13
Chapter3 Probability The definition of probability was given b Pierre Simon Laplace in 795 J.Cardan, an Italian physician and mathematician wrote the first book on probability named the book of games
More informationDef: The intersection of A and B is the set of all elements common to both set A and set B
Def: Sample Space the set of all possible outcomes Def: Element an item in the set Ex: The number "3" is an element of the "rolling a die" sample space Main concept write in Interactive Notebook Intersection:
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Statistics Homework Ch 5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability
More information12.6. Or and And Problems
12.6 Or and And Problems Or Problems P(A or B) = P(A) + P(B) P(A and B) Example: Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 is written on a separate piece of paper. The 10 pieces of paper are
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 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 informationCONDITIONAL PROBABILITY Assignment
State which the following events are independent and which are dependent.. Drawing a card from a standard deck of playing card and flipping a penny 2. Drawing two disks from an jar without replacement
More information2. The figure shows the face of a spinner. The numbers are all equally likely to occur.
MYP IB Review 9 Probability Name: Date: 1. For a carnival game, a jar contains 20 blue marbles and 80 red marbles. 1. Children take turns randomly selecting a marble from the jar. If a blue marble is chosen,
More informationStatistics and Probability
Lesson Statistics and Probability Name Use Centimeter Cubes to represent votes from a subgroup of a larger population. In the sample shown, the red cubes are modeled by the dark cubes and represent a yes
More information4. Are events C and D independent? Verify your answer with a calculation.
Honors Math 2 More Conditional Probability Name: Date: 1. A standard deck of cards has 52 cards: 26 Red cards, 26 black cards 4 suits: Hearts (red), Diamonds (red), Clubs (black), Spades (black); 13 of
More informationChapter 16. Probability. For important terms and definitions refer NCERT text book. (6) NCERT text book page 386 question no.
Chapter 16 Probability For important terms and definitions refer NCERT text book. Type I Concept : sample space (1)NCERT text book page 386 question no. 1 (*) (2) NCERT text book page 386 question no.
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 informationKey Concept Probability of Independent Events. Key Concept Probability of Mutually Exclusive Events. Key Concept Probability of Overlapping Events
154 Compound Probability TEKS FOCUS TEKS (1)(E) Apply independence in contextual problems. TEKS (1)(B) Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy,
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 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 informationGrade 7/8 Math Circles February 25/26, Probability
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Probability Grade 7/8 Math Circles February 25/26, 2014 Probability Centre for Education in Mathematics and Computing Probability is the study of how likely
More informationHARDER PROBABILITY. Two events are said to be mutually exclusive if the occurrence of one excludes the occurrence of the other.
HARDER PROBABILITY MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION LAW OF PROBABILITY Two events are said to be mutually exclusive if the occurrence of one excludes the occurrence of the other. Example Throwing
More information5.6. Independent Events. INVESTIGATE the Math. Reflecting
5.6 Independent Events YOU WILL NEED calculator EXPLORE The Fortin family has two children. Cam determines the probability that the family has two girls. Rushanna determines the probability that the family
More informationProbability CK12. Say Thanks to the Authors Click (No sign in required)
Probability CK12 Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit www.ck12.org
More informationFALL 2012 MATH 1324 REVIEW EXAM 4
FALL 01 MATH 134 REVIEW EXAM 4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the sample space for the given experiment. 1) An ordinary die
More informationInstructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to include your name and student numbers.
Math 3201 Unit 3 Probability Assignment 1 Unit Assignment Name: Part 1 Selected Response: Instructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to
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 informationTheoretical or Experimental Probability? Are the following situations examples of theoretical or experimental probability?
Name:Date:_/_/ Theoretical or Experimental Probability? Are the following situations examples of theoretical or experimental probability? 1. Finding the probability that Jeffrey will get an odd number
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 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 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 informationPROBABILITY.0 Concept Map Contents Page. Probability Of An Event. Probability Of Two Events. 4. Probability of Mutually Exclusive Events.4 Probability
PROGRAM DIDIK CEMERLANG AKADEMIK SPM ADDITIONAL MATHEMATICS FORM MODULE PROBABILITY PROBABILITY.0 Concept Map Contents Page. Probability Of An Event. Probability Of Two Events. 4. Probability of Mutually
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 informationnumber of favorable outcomes 2 1 number of favorable outcomes 10 5 = 12
Probability (Day 1) Green Problems Suppose you select a letter at random from the words MIDDLE SCHOOL. Find P(L) and P(not L). First determine the number of possible outcomes. There are 1 letters in the
More informationEmpirical (or statistical) probability) is based on. The empirical probability of an event E is the frequency of event E.
Probability and Statistics Chapter 3 Notes Section 31 I. Probability Experiments. A. When weather forecasters say There is a 90% chance of rain tomorrow, or a doctor says There is a 35% chance of a successful
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 informationUnit 19 Probability Review
. What is sample space? All possible outcomes Unit 9 Probability Review 9. I can use the Fundamental Counting Principle to count the number of ways an event can happen. 2. What is the difference between
More information2. Julie draws a card at random from a standard deck of 52 playing cards. Determine the probability of the card being a diamond.
Math 3201 Chapter 3 Review Name: Part I: Multiple Choice. Write the correct answer in the space provided at the end of this section. 1. Julie draws a card at random from a standard deck of 52 playing cards.
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 informationProbabilities of Simple Independent Events
Probabilities of Simple Independent Events Focus on After this lesson, you will be able to solve probability problems involving two independent events In the fairytale Goldilocks and the Three Bears, Goldilocks
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 informationIndependent Events. 1. Given that the second baby is a girl, what is the. e.g. 2 The probability of bearing a boy baby is 2
Independent Events 7. Introduction Consider the following examples e.g. E throw a die twice A first thrown is "" second thrown is "" o find P( A) Solution: Since the occurrence of Udoes not dependu on
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 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 informationProbability Quiz Review Sections
CP1 Math 2 Unit 9: Probability: Day 7/8 Topic Outline: Probability Quiz Review Sections 5.025.04 Name A probability cannot exceed 1. We express probability as a fraction, decimal, or percent. Probabilities
More informationExam III Review Problems
c Kathryn Bollinger and Benjamin Aurispa, November 10, 2011 1 Exam III Review Problems Fall 2011 Note: Not every topic is covered in this review. Please also take a look at the previous WeekinReviews
More informationNC MATH 2 NCFE FINAL EXAM REVIEW Unit 6 Probability
NC MATH 2 NCFE FINAL EXAM REVIEW Unit 6 Probability Theoretical Probability A tube of sweets contains 20 red candies, 8 blue candies, 8 green candies and 4 orange candies. If a sweet is taken at random
More informationUnit 14 Probability. Target 3 Calculate the probability of independent and dependent events (compound) AND/THEN statements
Target 1 Calculate the probability of an event Unit 14 Probability Target 2 Calculate a sample space 14.2a Tree Diagrams, Factorials, and Permutations 14.2b Combinations Target 3 Calculate the probability
More informationThis unit will help you work out probability and use experimental probability and frequency trees. Key points
Get started Probability This unit will help you work out probability and use experimental probability and frequency trees. AO Fluency check There are 0 marbles in a bag. 9 of the marbles are red, 7 are
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 informationContents 2.1 Basic Concepts of Probability Methods of Assigning Probabilities Principle of Counting  Permutation and Combination 39
CHAPTER 2 PROBABILITY Contents 2.1 Basic Concepts of Probability 38 2.2 Probability of an Event 39 2.3 Methods of Assigning Probabilities 39 2.4 Principle of Counting  Permutation and Combination 39 2.5
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 informationWhen combined events A and B are independent:
A Resource for reestanding Mathematics Qualifications A or B Mutually exclusive means that A and B cannot both happen at the same time. Venn Diagram showing mutually exclusive events: Aces The events
More informationSimple Probability. Arthur White. 28th September 2016
Simple Probability Arthur White 28th September 2016 Probabilities are a mathematical way to describe an uncertain outcome. For eample, suppose a physicist disintegrates 10,000 atoms of an element A, and
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 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 information1. A factory manufactures plastic bottles of 4 different sizes, 3 different colors, and 2 different shapes. How many different bottles are possible?
Unit 8 Quiz Review Short Answer 1. A factory manufactures plastic bottles of 4 different sizes, 3 different colors, and 2 different shapes. How many different bottles are possible? 2. A pizza corner offers
More informationProbability Unit 6 Day 3
Probability Unit 6 Day 3 Warmup: 1. If you have a standard deck of cards in how many different hands exists of: (Show work by hand but no need to write out the full factorial!) a) 5 cards b) 2 cards 2.
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 informationProbability Concepts and Counting Rules
Probability Concepts and Counting Rules Chapter 4 McGrawHill/Irwin Dr. Ateq Ahmed AlGhamedi Department of Statistics P O Box 80203 King Abdulaziz University Jeddah 21589, Saudi Arabia ateq@kau.edu.sa
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 informationChapter 3: PROBABILITY
Chapter 3 Math 3201 1 3.1 Exploring Probability: P(event) = Chapter 3: PROBABILITY number of outcomes favourable to the event total number of outcomes in the sample space An event is any collection of
More information, x {1, 2, k}, where k > 0. (a) Write down P(X = 2). (1) (b) Show that k = 3. (4) Find E(X). (2) (Total 7 marks)
1. The probability distribution of a discrete random variable X is given by 2 x P(X = x) = 14, x {1, 2, k}, where k > 0. Write down P(X = 2). (1) Show that k = 3. Find E(X). (Total 7 marks) 2. In a game
More information