PROBABILITY.0 Concept Map Contents Page. Probability Of An Event. Probability Of Two Events. 4. Probability of Mutually Exclusive Events.4 Probability


 Jesse Cummings
 3 years ago
 Views:
Transcription
1 PROGRAM DIDIK CEMERLANG AKADEMIK SPM ADDITIONAL MATHEMATICS FORM MODULE PROBABILITY
2 PROBABILITY.0 Concept Map Contents Page. Probability Of An Event. Probability Of Two Events. 4. Probability of Mutually Exclusive Events.4 Probability Of Independent Events.  SPM Questions Assessment test Answers 0
3 .0 CONCEPT MAP. Experiment A process to obtain observations The result of an experiment Possible outcomes Sample space, S The set of all possible outcomes An Event, A Mutually Exclusive Events Independent Event PROBABILITY P(A) = P(A B) = P(A) + P(B) P(A B) The complement of the event A. P(A ) = P(two events A and B that are mutually exclusive) is P(A B) = P(A) + P(B) A B= P(two or three independent events) P(A B) = P(A).P(B) P(A B) = P(A).P(B).P(C)
4 . PROBABILITY OF AN EVENT Example. Question Box A contains black balls, green balls and red balls. A ball is drawn at random from box A. Calculate the probability that the colour of the ball is (a) black not black (c) yellow Answer (a) Let R represent the event that a black ball is drawn. n(r) P(R) =. n(s) 0 P(the ball is not black) =P(R ) = P(R) = = 0 0 (c) P(the ball drawn is yellow) = 0. An event that is impossible to occur because there are no yellow balls in the box Exercises. No. Questions Answers. A box contains cards where each card is marked with an alphabet from the word TAMBAHAN. If a card is chosen at random, calculate the probability that (a) the card with the alphabet B is chosen. a card with vowel is chosen.. There are 4 red marbles and y green marbles in a bag. A marble is drawn at random from the box. Given that the probability of drawing a green is, calculate the value of y.. A bag contain x green marbles, y blue marbles and brown marbles. A marbles is drawn at random and the probability of getting a brown marble is. Write down the equation relating x and y.
5 . PROBABILITY OF THE TWO EVENTS Example. Question 4 9 The above figure shows six numbered cards. A card is chosen at random. Calculate the probability that the number on the chosen card (a) is a multiple of and a factor of is a multiple of or a factor of. Answer Let A represent the event that the number on the chosen card is a multiple of, and B represent the event that the number on the chosen card is a factor of. A = {,, 9}, n(a)= B = {,, 4, }, n(b) = 4 A B = {, } A B = {,, 4,, 9} (a) P(A B) =. P(A B) = Alternative method P(A B) = P(A) + P(B) P(A B) 4 = =. Exercises No. Questions Answers. A dice is thrown once. Calculate the probability that the score on the dice either an odd number or a prime number.. A card is chosen at random from a bag which contains the different letters of the alphabet. Find the probability that (a) the card chosen has a letter from the word BAHASA the card chosen is not a letter from the word KACA. The set X and Y are given as follows: X = {,,,, 9} Y = {, 4, } A number is chosen at random from set X and another number from set Y. Calculate the probability that the sum of the number is 9 or the product of the number is. 4
6 . PROBABILITY OF MUTUALLY EXCLUSIVE EVENTS Example. Question A box contains red balls, yellow balls and 4 green balls. A ball is chosen at random from the box. Calculate the probability that the balls drawn neither a yellow nor a green. P (yellow) =. Solution P(green) = 4 P(yellow or green) = + 4 =. Exercises No. Questions Answers. A fair dice is thrown. Let x be the event when the dice shows and Y be the event when the dice shows an even number. (a) Are the two events mutually exclusive? Find the probability that or even number is the outcome.. A marble is drawn at random from a box containing black marbles, 4 green marbles and white marbles. (a) What is the probability of drawing a black or a green marble? What is the probability of drawing neither a black nor a white marble?. Box T contains three card numbered, and. Box U contains three card numbered, and 4. A card is drawn at random from box T and at the same time, another card is drawn from box U. Calculate the probability that the two numbers drawn have the same value or a sum of.
7 .4 PROBABILITY OF INDEPENDENT EVENTS Example 4 No Questions Solutions. 4 Black Box C contains 4 black marbles and Black yellow marbles. A marbles is chosen at random from box C, its colour is Yellow 0 noted and the marbles is noted and the 4 marbles is returned to the box. Then a Black 0 second marbles is chosen. Determine 0 Yellow the probability that Yellow (a) (c) both the marbles are black. the two balls are of different colours. at least one of the balls chosen is yellow (a) P(black black)= = 0 0 P(same colours) = P(black black) + P(yellow yellow) 4 = + = (c) P(both blacks) = = 0. The probability that participants K, L and M will win a dancing contest are, and respectively. If the events of each participant winning are independent, calculate the probability that (a) only L wins, two participants win. (a) K L M Win Win ck Win ck lose k Win Lose ck lose lose Win k Lose P(only L wins) = P(K L M ) = P(K ) P(L) P(M ). = Win ck lose Win ck lose = 4 P( participants win) = P(K L M ) + P(K L M) + P(K L M). = =
8 Exercises 4 No. Questions Solutions. A bag has green cubes and red cubes. Two cubes are drawn from the bag at random, one after the other, without replacement. Calculate the probability that the green cube and a red cube are drawn.. Hasan competes with John in the finals of a squash competition. The competition will end when a player wins three sets. The probability that Hasan will win any set is. Calculate the probability that (a) the competition ends after only three sets. Hashim is the winner after playing four sets.. Bag B contains red balls and yellow balls. A ball is drawn at random from bag B. The ball is then put into bag D that contains 4 red balls and yellow balls. After that, another ball is drawn at random from bag D. Calculate the probability that the ball drawn from bag B is of the same colour as the ball drawn from bag D.
9 PAST YEAR QUESTIONS. No. Questions Solutions. A box contains white marbles and k black marbles. If a marble is picked randomly from the box, the probability of getting a black marble is. Find the value of k. SPM 04(No.4 / Paper ).. Table shows the number of coloured cards in a box Colour Number of cards Black Blue 4 Yellow Two cards are drawn at random from the box. Find the probability that both cards are of the same colour. SPM.0(No. 4 / Paper ) ASSESSMENT TEST No. Questions Solutions. There are 4 blue balls and y red balls in the box. A ball is drawn at random from the box. Given that the probability of drawing a red ball is, calculate the value of y.. Two dice, one white and one black, are thrown together. Calculate the probability that the score on the white dice is twice the score on the black dice.
10 No. Questions Solutions. A box contains 40 marbles. The colours of the marbles are green and red. If a marble is drawn at random from the box, the probability that a green marble is drawn is. Calculate (a) the number of red marbles in the box, the number of red marbles that have to be added to the box such that the probability to drawn a red marble becomes. 4. Bag I contains blue marbles and black marbles while bag II contains blue marbles and 4 black marbles. If a marble is chosen at random from each bag, calculate the probability that (a) both the marbles are black, the marble from bag I is blue and the marble from bag II is black. (c) At least one of the marbles chosen is black.. Two sixfaced unbiased dice are thrown together. Calculate the probability that (a) the sum of two numbers is. The difference of two numbers is, (c) The sum of two numbers is or The difference of two numbers is.. In a soccer match between team B and team D, the result can be a draw or a win for team B or a win for team D. The probability that team B and team D will win are and. In two matches, calculates the probability that team B wins once and draw once. 9
11 ANSWERS Exercises. (a).. x + y = PAST YEAR QUESTION Exercises.. (a). 4 Exercise. (a) Yes. (a) ASSESSMENT TEST (a). (a). (c) 9 Exercise (a). 0
STANDARD 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 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. 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 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 informationMath : Probabilities
20 20. Probability EPProgram  Strisuksa School  Roiet Math : Probabilities Dr.Wattana Toutip  Department of Mathematics Khon Kaen University 200 :Wattana Toutip wattou@kku.ac.th http://home.kku.ac.th/wattou
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 informationChapterwise questions. Probability. 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail.
Probability 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail. 2. 26 cards marked with English letters A to Z (one letter on each card) are shuffled well. If one
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 informationOutcomes: The outcomes of this experiment are yellow, blue, red and green.
(Adapted from http://www.mathgoodies.com/) 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
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 informationD1 Probability of One Event
D Probability of One Event Year 3/4. I have 3 bags of marbles. Bag A contains 0 marbles, Bag B contains 20 marbles and Bag C contains 30 marbles. One marble in each bag is red. a) Join up each statement
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 informationRevision Topic 17: Probability Estimating probabilities: Relative frequency
Revision Topic 17: Probability Estimating probabilities: Relative frequency Probabilities can be estimated from experiments. The relative frequency is found using the formula: number of times event occurs.
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 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 informationQ1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together.
Required Probability = where Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together. Solution: As girls are always together so they are considered as a group.
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 informationClassical Definition of Probability Relative Frequency Definition of Probability Some properties of Probability
PROBABILITY Recall that in a random experiment, the occurrence of an outcome has a chance factor and cannot be predicted with certainty. Since an event is a collection of outcomes, its occurrence cannot
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 informationProbability Review Questions
Probability Review Questions Short Answer 1. State whether the following events are mutually exclusive and explain your reasoning. Selecting a prime number or selecting an even number from a set of 10
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 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 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 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 informationDiamond ( ) (Black coloured) (Black coloured) (Red coloured) ILLUSTRATIVE EXAMPLES
CHAPTER 15 PROBABILITY Points to Remember : 1. In the experimental approach to probability, we find the probability of the occurence of an event by actually performing the experiment a number of times
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 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 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 informationModule 4 Project Maths Development Team Draft (Version 2)
5 Week Modular Course in Statistics & Probability Strand 1 Module 4 Set Theory and Probability It is often said that the three basic rules of probability are: 1. Draw a picture 2. Draw a picture 3. Draw
More informationSection 6.5 Conditional Probability
Section 6.5 Conditional Probability Example 1: An urn contains 5 green marbles and 7 black marbles. Two marbles are drawn in succession and without replacement from the urn. a) What is the probability
More information2. The value of the middle term in a ranked data set is called: A) the mean B) the standard deviation C) the mode D) the median
1. An outlier is a value that is: A) very small or very large relative to the majority of the values in a data set B) either 100 units smaller or 100 units larger relative to the majority of the values
More informationStat210 WorkSheet#2 Chapter#2
1. When rolling a die 5 times, the number of elements of the sample space equals.(ans.=7,776) 2. If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet,
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 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. 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 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 M.K. HOME TUITION. Mathematics Revision Guides. Level: GCSE Foundation Tier
Mathematics Revision Guides Probability Page 1 of 18 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier PROBABILITY Version: 2.1 Date: 08102015 Mathematics Revision Guides Probability
More informationExercise Class XI Chapter 16 Probability Maths
Exercise 16.1 Question 1: Describe the sample space for the indicated experiment: A coin is tossed three times. A coin has two faces: head (H) and tail (T). When a coin is tossed three times, the total
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 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 information1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 100 calculators is tested.
1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 0 calculators is tested. Write down the expected number of faulty calculators in the sample. Find
More informationCONTENTS CONTENTS PAGES 11.0 CONCEPT MAP A. PERMUTATIONS a EXERCISE A B. COMBINATIONS a EXERCISE B PAST YEAR SPM
PROGRAM DIDIK CEMERLANG AKADEMIK SPM ADDITIONAL MATHEMATICS FORM 5 MODULE 11 PERMUTATIONS AND COMBINATIONS 0 CONTENTS CONTENTS PAGES 11.0 CONCEPT MAP 2 11.1 A. PERMUTATIONS 3 11.1a EXERCISE A.1 3 11.2
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 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 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 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 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 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 informationWorksheets for GCSE Mathematics. Probability. mrmathematics.com Maths Resources for Teachers. Handling Data
Worksheets for GCSE Mathematics Probability mrmathematics.com Maths Resources for Teachers Handling Data Probability Worksheets Contents Differentiated Independent Learning Worksheets Probability Scales
More informationPROBABILITY Case of cards
WORKSHEET NO1 PROBABILITY Case of cards WORKSHEET NO2 Case of two die Case of coins WORKSHEET NO3 1) Fill in the blanks: A. The probability of an impossible event is B. The probability of a sure
More informationClass XII Chapter 13 Probability Maths. Exercise 13.1
Exercise 13.1 Question 1: Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E F) = 0.2, find P (E F) and P(F E). It is given that P(E) = 0.6, P(F) = 0.3, and P(E F) = 0.2 Question 2:
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 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 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 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 informationSection Introduction to Sets
Section 1.1  Introduction to Sets Definition: A set is a welldefined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase
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 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 informationEnrichment. Suppose that you are given this information about rolling a number cube.
ate  Working ackward with Probabilities Suppose that you are given this information about rolling a number cube. P() P() P() an you tell what numbers are marked on the faces of the cube Work backward.
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 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 informationNorth Seattle Community College Winter ELEMENTARY STATISTICS 2617 MATH Section 05, Practice Questions for Test 2 Chapter 3 and 4
North Seattle Community College Winter 2012 ELEMENTARY STATISTICS 2617 MATH 109  Section 05, Practice Questions for Test 2 Chapter 3 and 4 1. Classify each statement as an example of empirical probability,
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 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 informationProbability Worksheet Yr 11 Maths B Term 4
Probability Worksheet Yr Maths B Term A die is rolled. What is the probability that the number is an odd number or a? P(odd ) Pr(odd or a + 6 6 6 A set of cards is numbered {,, 6}. A card is selected at
More informationMutually Exclusive Events
Mutually Exclusive Events Suppose you are rolling a sixsided die. What is the probability that you roll an odd number and you roll a 2? Can these both occur at the same time? Why or why not? Mutually
More informationCSC/MATA67 Tutorial, Week 12
CSC/MATA67 Tutorial, Week 12 November 23, 2017 1 More counting problems A class consists of 15 students of whom 5 are prefects. Q: How many committees of 8 can be formed if each consists of a) exactly
More informationProbability I Sample spaces, outcomes, and events.
Probability I Sample spaces, outcomes, and events. When we perform an experiment, the result is called the outcome. The set of possible outcomes is the sample space and any subset of the sample space is
More informationProbability Study Guide Date Block
Probability Study Guide Name Date Block In a regular deck of 52 cards, face cards are Kings, Queens, and Jacks. Find the following probabilities, if one card is drawn: 1)P(not King) 2) P(black and King)
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 information7 5 Compound Events. March 23, Alg2 7.5B Notes on Monday.notebook
7 5 Compound Events At a juice bottling factory, quality control technicians randomly select bottles and mark them pass or fail. The manager randomly selects the results of 50 tests and organizes the data
More informationb. 2 ; the probability of choosing a white d. P(white) 25, or a a. Since the probability of choosing a
Applications. a. P(green) =, P(yellow) = 2, or 2, P(red) = 2 ; three of the four blocks are not red. d. 2. a. P(green) = 2 25, P(purple) = 6 25, P(orange) = 2 25, P(yellow) = 5 25, or 5 2 6 2 5 25 25 25
More informationP(X is on ) Practice Test  Chapter 13. BASEBALL A baseball team fields 9 players. How many possible batting orders are there for the 9 players?
Point X is chosen at random on. Find the probability of each event. P(X is on ) P(X is on ) BASEBALL A baseball team fields 9 players. How many possible batting orders are there for the 9 players? or 362,880.
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 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 informationChapter 1. Probability
Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.
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 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 informationMathematics 3201 Test (Unit 3) Probability FORMULAES
Mathematics 3201 Test (Unit 3) robability Name: FORMULAES ( ) A B A A B A B ( A) ( B) ( A B) ( A and B) ( A) ( B) art A : lace the letter corresponding to the correct answer to each of the following in
More informationRaise your hand if you rode a bus within the past month. Record the number of raised hands.
166 CHAPTER 3 PROBABILITY TOPICS Raise your hand if you rode a bus within the past month. Record the number of raised hands. Raise your hand if you answered "yes" to BOTH of the first two questions. Record
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 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 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 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 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 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 informationMutually Exclusive Events Algebra 1
Name: Mutually Exclusive Events Algebra 1 Date: Mutually exclusive events are two events which have no outcomes in common. The probability that these two events would occur at the same time is zero. Exercise
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 informationAnswer each of the following problems. Make sure to show your work.
Answer each of the following problems. Make sure to show your work. 1. A board game requires each player to roll a die. The player with the highest number wins. If a player wants to calculate his or her
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 information136 Probabilities of Mutually Exclusive Events
Determine whether the events are mutually exclusive or not mutually exclusive. Explain your reasoning. 1. drawing a card from a standard deck and getting a jack or a club The jack of clubs is an outcome
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 Date. Probability of Disjoint and Overlapping Events For use with Exploration 12.4
12.4 Probability of Disjoint and Overlapping Events For use with Exploration 12.4 Essential Question How can you find probabilities of disjoint and overlapping events? Two events are disjoint, or mutually
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 informationPage 1 of 22. Website: Mobile:
Exercise 15.1 Question 1: Complete the following statements: (i) Probability of an event E + Probability of the event not E =. (ii) The probability of an event that cannot happen is. Such as event is called.
More informationExam 2 Review F09 O Brien. Finite Mathematics Exam 2 Review
Finite Mathematics Exam Review Approximately 5 0% of the questions on Exam will come from Chapters, 4, and 5. The remaining 70 75% will come from Chapter 7. To help you prepare for the first part of the
More information12.1 Practice A. Name Date. In Exercises 1 and 2, find the number of possible outcomes in the sample space. Then list the possible outcomes.
Name Date 12.1 Practice A In Exercises 1 and 2, find the number of possible outcomes in the sample space. Then list the possible outcomes. 1. You flip three coins. 2. A clown has three purple balloons
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 information, the of all of a probability experiment. consists of outcomes. (b) List the elements of the event consisting of a number that is greater than 4.
41 Sample Spaces and Probability as a general concept can be defined as the chance of an event occurring. In addition to being used in games of chance, probability is used in the fields of,, and forecasting,
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 information