XXII Probability. 4. The odds of being accepted in Mathematics at McGill University are 3 to 8. Find the probability of being accepted.


 Gregory Atkinson
 3 years ago
 Views:
Transcription
1 MATHEMATICS 20BNJ05 Topics in Mathematics Martin Huard Winter 204 XXII Probability. Find the sample space S along with n S. a) The face cards are removed from a regular deck and then card is selected from this set of 2 face cards. A box contains three marbles of different colors, blue, red and green. Two balls are drawn at random (without replacement). A box contains three marbles of different colors, blue, red and green. Two balls are drawn at random (with replacement). d) Two dice are rolled, and the sum of their dots is observed. e) Two dice are rolled, and the product of their dots is observed. f) Three coins are tossed and the outcome is recorded. 2. A single die is rolled. Find the probability the number on top is: a) a 3. an odd number. a number less than 5. d) a number no more than Two dice are rolled, where one is black and the other is white. Find the following probabilities. a) P(white die is an odd number) P(sum is 6) P(both dice show odd numbers) d) P(# on black die > # on white die) 4. The odds of being accepted in Mathematics at McGill University are 3 to 8. Find the probability of being accepted. 5. A box contains 3 marbles, a red, a blue and a green marble. In two marbles are picked at random, what is the probability that a) one is red and the other is green? both are red? 6. A card is drawn from a standard deck of 52 cards. Find the following probabilities. a) P( King ) P( club ) P( black card) d) P( Face card ) 7. A group of 50 randomly selected CEOs was tested for personality type. The following table gives the results of this survey. Type A Type B Men Women If one CEO is selected at random from this group, find the probability that this CEO a) has a type A personality is a women is a women with a type A personality
2 8. The academic adviser of a college informs us that in his college of 4000 students, 500 students are currently enrolled in a philosophy class and 550 in a mathematics class. If 220 students are in a philosophy and a mathematics class, find the probability that if a student is selected at random, he will be in: a) only a philosophy class only a mathematics class a least one of the two classes. 9. The newsletter of a College announced that 75 students are in a math or poetry club. If the math club has 92 members, with 35 also in the poetry club, what is the probability that if a student is picked at random a) he will be in the math club only. he will be in the poetry club only. he will be in both clubs. 0. A group of 90 freshman engineering students at a large university was surveyed with the following results. of the students read Scientific American 8 read Popular Mechanics 50 read Mathematics Magazine 3 read Scientific American and Popular Mechanics read Popular Mechanics and Mathematics Magazine 3 read Scientific American and Mathematics Magazine 9 read all three Using this data, determine the probability that if a student is chosen at random, he will read a) none of the publications? Mathematics Magazine only? How many read Scientific American and Popular Mechanics, but not Mathematics Magazine?. A survey on a group of 00 College students showed that 8 of them have a motorcycle, 20 have a car, 48 have a bicycle and 38 have neither a motorcycle, a car or a bicycle. No one has at the same time a motorcycle and a car. What is the probability that a student chosen at random has a bicycle and either a car or a motorcycle? 2. Two cards are drawn from a deck of 52 cards. What is the probability that a) both are clubs both are Jacks. 3. A single card is drawn from a deck of 52 cards. What is the probability that the card is a) a king of diamonds? a king or a diamond? a face card? d) a red face card? e) not an ace? 4. An urn contains 20 marbles, of which 5 are red, 6 are blue, 7 are yellow and 2 are green. If two marbles are chosen at random, what is the probability that a) both are blue? one is blue and the other is red? both are of the same color? d)the two marbles are not the same color? Winter 204 Martin Huard 2
3 5. In a refugee camp in Rwanda, it was found that 90% of the refugees came to escape political oppression, 80% came to escape abject poverty, and 70% came to escape both. What is the probability that a refugee in the camp was neither poor nor seeking political asylum? 6. A survey conducted about job satisfaction showed that 20% of workers are not happy with their current job. Assume that this result is true for the population of all workers. Two workers are selected at random, and it is observed whether or not they are happy with their current jobs. Find the probability that in this sample of two workers, a) both are not happy with their current jobs. at least one of them is happy with the current job. 7. Suppose a birth control pill is 99% effective in preventing pregnancy. a) What is the probability that none of 00 women using the pill will become pregnant? What is the probability that at least one woman per 00 users will become pregnant? 8. A company has installed a generator to back up the power in case there is a power failure. The probability that there will be a power failure during a snowstorm is The probability that the generator will stop working during a snowstorm is What is the probability that during a snowstorm the company will lose both sources of power?. An old age home employs 65 people. Eight of the 30 men and 2 of the 35 women are nurses. What is the probability that an employee picked at random is a man or is a nurse? 20. Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the twoway classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same, or worse off than their parents. Education Level High school or CEGEP More than less CEGEP Better off Same Worse off Suppose one adult is selected at random from these 2000 adults. Find the following. a) P(better off or CEGEP) P(More that CEGEP or worse off) P(better off or worse off) d) P(better off given CEGEP) e) Are the events better off and CEGEP independent? f) Are the events better off and CEGEP mutually exclusive? 2. What is the probability that in a group of 4 students, no two students have their birthday in the same month? 22. If a committee of five is chosen from a pool of 2 candidates, what is the probability that two of the candidates, Galois and Abel, will not sit on the committee together? Winter 204 Martin Huard 3
4 23. In a group of 2 SLC students, 5 are in science, 4 in social science, and 3 in business. If a group of four is chosen, what is the probability that the group a) Will consist of only science students? Will have at least one science student? At least one student from each program? 24. A coin is tossed eight times. Find the probability of having a) No Heads At least one Head Exactly two heads d) At least two Heads 25. The odds that Robin will hit a target with his arrow is 4 to. If he shoots five arrows, what is the probability that a) he will hit the target only with his fifth arrow? He will hit the target at least once? He will hit the target with at least four arrows? d) He will hit the target with exactly three arrows? 26. It is estimated that 5% of a large consignment of eggs in a certain supermarket are broken. a) What is the probability that a customer who randomly selects a dozen of these eggs receives at least one broken egg? What is the probability that a customer who selects these eggs at random will have to check more than three cartons before finding a carton without any broken eggs? (Each carton contains a dozen eggs). 27. Alex, Bill and Joe each in turn toss a balanced coin. The first one to throw a head wins. a) What are their respective chances of winning if each tosses only one time? What are their respective chances of winning if they continue, when there is no winner, giving a maximum of two tosses each? 28. The probability that a certain door is locked is 0.6. The key to the door is one of five unidentified keys hanging of a key rack. Two keys are randomly selected before approaching the door. What is the probability that the door may be opened without returning for another key? 29. At SLC, 60% of students in science are in the Pure and Applied profile. Of these, 95% love mathematics, while 75% of students in the Health profile love mathematics. Find the probability that a science student chosen at random a) loves math and is in the Health profile loves math 30. A smoothtalking young man has a /3 probability of talking a policeman out of giving him a speeding ticket. The probability that he is stopped for speeding during a given weekend is ½. Find the probability that he will receive no speeding tickets a) on a given weekend? on 3 consecutive weekends? 3. Five black balls and four white balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a white ball a) if the second ball is drawn without replacing the first? If the first ball is replaced before the second is drawn? Winter 204 Martin Huard 4
5 32. Two cards are drawn in succession without replacement of a deck of 52 cards. a) What is the probability that the first card is a heart given that the second card is a heart? What is the probability that the first card is a heart given the second card is a diamond? What is the probability that the first card is a jack given that the second card is an ace? 33. Urn A contains four white and six black balls. Urn B contains three white and five black balls. A ball is drawn from urn A and then transferred to urn B. A ball is then drawn from urn B. a) What is the probability that the transferred ball was white given that the second ball drawn was white? What is the probability that the transferred ball was black given that the second ball drawn was white? 34. As accounts manager in your company, you classify 75% of your customers as "good credit" and the rest as "risky credit" depending on their credit rating. Customers in the "risky" category allow their accounts to go overdue 55% of the time on average, whereas those in the "good" category allow their accounts to become overdue only 0% of the time. What percentage of overdue accounts is held by customers in the "risky credit" category? 35. A witness sees a crime involving a taxi in Cabcity. The witness says that the taxi is green. It is known from previous research that witnesses are correct 80% of the time when making such statements. The police also know that 75% of the taxis in Cabcity are green, the other 25% being blue. What is the probability that a green taxi was involved in the crime? 36. A car insurance company has compiled the following table concerning the age distribution of its clients. Age % of clients % of group who are made a claim last year 25 and under and over a) What is the probability that a client selected at random made a claim last year? If a client made a claim last year, what is the probability that he or she is in the 25 and under age bracket? 37. Suppose the weather in a certain city is either rainy or sunny. Past records show that if it is sunny today, then it will be sunny tomorrow with a probability of 0.8 and if it is rainy today, then it will be rainy tomorrow with a probability of 0.7. Today is a sunny day. a) What is the probability it will be sunny n days from now? What proportion of days are sunny? 38. Sheldon either reads a math book or a physics book. If reads a math book, the probability the next book will be a math one is ¾, and if he reads a physics book, the probability the next one will be a math one is ½. a) What is the probability he will read a math book n books from now if he is currently reading a physics book. What proportion of books read are math books? Winter 204 Martin Huard 5
6 ANSWERS. a) S = { J, J, J, J, Q, Q, Q, Q, K, K, K, K } n S 2 S BR, BG, RB, RG, GB, GR n S 6 S BB, BR, BG, RB, RR, RG, GB, GR, GG n S 9 d) S 2,3, 4,5,6,7,8,9,0,,2 n S e) S, 2,3, 4,5,6,8,9,0,2,5,6,8, 20, 24, 25,30,36 n S 8 f) S HHH, HHT, HTH, HTT, THH, THT, TTH, TTT n S 8 2. a) d) 2 3. a) d) a) a) d) a) a) a) a) d) a) d) a) a) a) d) a) a) 7 22 e) e) No since P(better off) = 0 P(better off given CEGEP) = f) No since P(better off and CEGEP) = a) a) a) d) 25. a) a) A = 2 B = 4 J = 8 A = B C 29. a) a) a) a) a) a) a) P M n a) 2 n n P Sn d) Winter 204 Martin Huard 6
1. Two cards are drawn from a deck of 52 cards. What is the probability that a) both are clubs b) both are Jacks.
MATHEMATICS 360255LW Quantitative Methods II Philip Foth 1. Two cards are drawn from a deck of 52 cards. What is the probability that a) both are clubs both are Jacks. 2. A single card is drawn from
More informationMath 146 Statistics for the Health Sciences Additional Exercises on Chapter 3
Math 46 Statistics for the Health Sciences Additional Exercises on Chapter 3 Student Name: Find the indicated probability. ) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH
More informationProbability and Statistics. Copyright Cengage Learning. All rights reserved.
Probability and Statistics Copyright Cengage Learning. All rights reserved. 14.2 Probability Copyright Cengage Learning. All rights reserved. Objectives What Is Probability? Calculating Probability by
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 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 informationFdaytalk.com. Outcomes is probable results related to an experiment
EXPERIMENT: Experiment is Definite/Countable probable results Example: Tossing a coin Throwing a dice OUTCOMES: Outcomes is probable results related to an experiment Example: H, T Coin 1, 2, 3, 4, 5, 6
More informationChapter 8: Probability: The Mathematics of Chance
Chapter 8: Probability: The Mathematics of Chance FreeResponse 1. A spinner with regions numbered 1 to 4 is spun and a coin is tossed. Both the number spun and whether the coin lands heads or tails is
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 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 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 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 informationThe probability setup
CHAPTER 2 The probability setup 2.1. Introduction and basic theory We will have a sample space, denoted S (sometimes Ω) that consists of all possible outcomes. For example, if we roll two dice, the sample
More informationMath 147 Elementary Probability/Statistics I Additional Exercises on Chapter 4: Probability
Math 147 Elementary Probability/Statistics I Additional Exercises on Chapter 4: Probability Student Name: Find the indicated probability. 1) If you flip a coin three times, the possible outcomes are HHH
More informationUNIT 4 APPLICATIONS OF PROBABILITY Lesson 1: Events. Instruction. Guided Practice Example 1
Guided Practice Example 1 Bobbi tosses a coin 3 times. What is the probability that she gets exactly 2 heads? Write your answer as a fraction, as a decimal, and as a percent. Sample space = {HHH, HHT,
More informationTEST A CHAPTER 11, PROBABILITY
TEST A CHAPTER 11, PROBABILITY 1. Two fair dice are rolled. Find the probability that the sum turning up is 9, given that the first die turns up an even number. 2. Two fair dice are rolled. Find the probability
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 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 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 informationThe probability setup
CHAPTER The probability setup.1. Introduction and basic theory We will have a sample space, denoted S sometimes Ω that consists of all possible outcomes. For example, if we roll two dice, the sample space
More informationSTAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes
STAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes Pengyuan (Penelope) Wang May 25, 2011 Review We have discussed counting techniques in Chapter 1. (Principle
More informationMATH CALCULUS & STATISTICS/BUSN  PRACTICE EXAM #1  SPRING DR. DAVID BRIDGE
MATH 205  CALCULUS & STATISTICS/BUSN  PRACTICE EXAM #  SPRING 2006  DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Tell whether the statement is
More informationName: Class: Date: Probability/Counting Multiple Choice PreTest
Name: _ lass: _ ate: Probability/ounting Multiple hoice PreTest Multiple hoice Identify the choice that best completes the statement or answers the question. 1 The dartboard has 8 sections of equal area.
More informationSTAT 155 Introductory Statistics. Lecture 11: Randomness and Probability Model
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Lecture 11: Randomness and Probability Model 10/5/06 Lecture 11 1 The Monty Hall Problem Let s Make A Deal: a game show
More informationProbability Exercise 2
Probability Exercise 2 1 Question 9 A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will
More informationFunctional Skills Mathematics
Functional Skills Mathematics Level Learning Resource Probability D/L. Contents Independent Events D/L. Page  Combined Events D/L. Page  9 West Nottinghamshire College D/L. Information Independent Events
More 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 informationSTOR 155 Introductory Statistics. Lecture 10: Randomness and Probability Model
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Lecture 10: Randomness and Probability Model 10/6/09 Lecture 10 1 The Monty Hall Problem Let s Make A Deal: a game show
More informationProbability QUESTIONS Principles of Math 12  Probability Practice Exam 1
Probability QUESTIONS Principles of Math  Probability Practice Exam www.math.com Principles of Math : Probability Practice Exam Use this sheet to record your answers:... 4... 4... 4.. 6. 4.. 6. 7..
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 information4.3 Rules of Probability
4.3 Rules of Probability If a probability distribution is not uniform, to find the probability of a given event, add up the probabilities of all the individual outcomes that make up the event. Example:
More 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 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 information3 The multiplication rule/miscellaneous counting problems
Practice for Exam 1 1 Axioms of probability, disjoint and independent events 1 Suppose P (A 0, P (B 05 (a If A and B are independent, what is P (A B? What is P (A B? (b If A and B are disjoint, what is
More informationLesson 10: Using Simulation to Estimate a Probability
Lesson 10: Using Simulation to Estimate a Probability Classwork In previous lessons, you estimated probabilities of events by collecting data empirically or by establishing a theoretical probability model.
More informationAP Statistics Ch InClass Practice (Probability)
AP Statistics Ch 1415 InClass Practice (Probability) #1a) A batter who had failed to get a hit in seven consecutive times at bat then hits a gamewinning home run. When talking to reporters afterward,
More informationChapter 1: Sets and Probability
Chapter 1: Sets and Probability Section 1.31.5 Recap: Sample Spaces and Events An is an activity that has observable results. An is the result of an experiment. Example 1 Examples of experiments: Flipping
More informationHomework #119: Use the Counting Principle to answer the following questions.
Section 4.3: Tree Diagrams and the Counting Principle Homework #119: Use the Counting Principle to answer the following questions. 1) If two dates are selected at random from the 365 days of the year
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 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 information1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2)
Math 1090 Test 2 Review Worksheet Ch5 and Ch 6 Name Use the following distribution to answer the question. 1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2) 3) Estimate
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 information1 2step and other basic conditional probability problems
Name M362K Exam 2 Instructions: Show all of your work. You do not have to simplify your answers. No calculators allowed. 1 2step and other basic conditional probability problems 1. Suppose A, B, C are
More information3 The multiplication rule/miscellaneous counting problems
Practice for Exam 1 1 Axioms of probability, disjoint and independent events 1. Suppose P (A) = 0.4, P (B) = 0.5. (a) If A and B are independent, what is P (A B)? What is P (A B)? (b) If A and B are disjoint,
More informationChapter 11: Probability and Counting Techniques
Chapter 11: Probability and Counting Techniques Diana Pell Section 11.3: Basic Concepts of Probability Definition 1. A sample space is a set of all possible outcomes of an experiment. Exercise 1. An experiment
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 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 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 informationMath 227 Elementary Statistics. Bluman 5 th edition
Math 227 Elementary Statistics Bluman 5 th edition CHAPTER 4 Probability and Counting Rules 2 Objectives Determine sample spaces and find the probability of an event using classical probability or empirical
More informationRANDOM EXPERIMENTS AND EVENTS
Random Experiments and Events 18 RANDOM EXPERIMENTS AND EVENTS In daytoday life we see that before commencement of a cricket match two captains go for a toss. Tossing of a coin is an activity and getting
More informationContemporary Mathematics Math 1030 Sample Exam I Chapters Time Limit: 90 Minutes No Scratch Paper Calculator Allowed: Scientific
Contemporary Mathematics Math 1030 Sample Exam I Chapters 1315 Time Limit: 90 Minutes No Scratch Paper Calculator Allowed: Scientific Name: The point value of each problem is in the lefthand margin.
More informationProbability and Counting Techniques
Probability and Counting Techniques Diana Pell (Multiplication Principle) Suppose that a task consists of t choices performed consecutively. Suppose that choice 1 can be performed in m 1 ways; for each
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More 9.9.3 Practice Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. ) In how many ways can you answer the questions on
More informationProbability Homework
Probability Homework Section P 1. A pair of fair dice are tossed. What is the conditional probability that the two dice are the same given that the sum equals 8? 2. A die is tossed. a) Find the probability
More informationSection 11.4: Tree Diagrams, Tables, and Sample Spaces
Section 11.4: Tree Diagrams, Tables, and Sample Spaces Diana Pell Exercise 1. Use a tree diagram to find the sample space for the genders of three children in a family. Exercise 2. (You Try!) A soda machine
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 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 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 informationUse a tree diagram to find the number of possible outcomes. 2. How many outcomes are there altogether? 2.
Use a tree diagram to find the number of possible outcomes. 1. A pouch contains a blue chip and a red chip. A second pouch contains two blue chips and a red chip. A chip is picked from each pouch. The
More informationLC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following.
A Ryan LC OL Probability ARNMaths.weebly.com Learning Outcomes As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. Counting List outcomes of an experiment Apply
More informationCHAPTER 2 PROBABILITY. 2.1 Sample Space. 2.2 Events
CHAPTER 2 PROBABILITY 2.1 Sample Space A probability model consists of the sample space and the way to assign probabilities. Sample space & sample point The sample space S, is the set of all possible outcomes
More information1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building?
1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building? 2. A particular brand of shirt comes in 12 colors, has a male version and a female version,
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Mathematical Ideas Chapter 2 Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) In one town, 2% of all voters are Democrats. If two voters
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 informationProbability of Independent and Dependent Events
706 Practice A Probability of In and ependent Events ecide whether each set of events is or. Explain your answer.. A student spins a spinner and rolls a number cube.. A student picks a raffle ticket from
More informationProbability. Dr. Zhang Fordham Univ.
Probability! Dr. Zhang Fordham Univ. 1 Probability: outline Introduction! Experiment, event, sample space! Probability of events! Calculate Probability! Through counting! Sum rule and general sum rule!
More informationName: Spring P. Walston/A. Moore. Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams FCP
Name: Spring 2016 P. Walston/A. Moore Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams 10 13 FCP 11 16 Combinations/ Permutations Factorials 12 22 13 20 Intro to Probability
More informationProbability Assignment
Name Probability Assignment Student # Hr 1. An experiment consists of spinning the spinner one time. a. How many possible outcomes are there? b. List the sample space for the experiment. c. Determine the
More informationMTH 103 H Final Exam. 1. I study and I pass the course is an example of a. (a) conjunction (b) disjunction. (c) conditional (d) connective
MTH 103 H Final Exam Name: 1. I study and I pass the course is an example of a (a) conjunction (b) disjunction (c) conditional (d) connective 2. Which of the following is equivalent to (p q)? (a) p q (b)
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 informationThe point value of each problem is in the lefthand margin. You must show your work to receive any credit, except on problems 1 & 2. Work neatly.
Introduction to Statistics Math 1040 Sample Exam II Chapters 57 4 Problem Pages 4 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of
More informationEECS 203 Spring 2016 Lecture 15 Page 1 of 6
EECS 203 Spring 2016 Lecture 15 Page 1 of 6 Counting We ve been working on counting for the last two lectures. We re going to continue on counting and probability for about 1.5 more lectures (including
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 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 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 informationProbability: Part 1 1/28/16
Probability: Part 1 1/28/16 The Kind of Studies We Can t Do Anymore Negative operant conditioning with a random reward system Addictive behavior under a random reward system FBJ murine osteosarcoma viral
More informationCHAPTER 7 Probability
CHAPTER 7 Probability 7.1. Sets A set is a welldefined collection of distinct objects. Welldefined means that we can determine whether an object is an element of a set or not. Distinct means that we can
More informationI. WHAT IS PROBABILITY?
C HAPTER 3 PROAILITY Random Experiments I. WHAT IS PROAILITY? The weatherman on 10 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and
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 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 informationChapter 11: Probability and Counting Techniques
Chapter 11: Probability and Counting Techniques Diana Pell Section 11.1: The Fundamental Counting Principle Exercise 1. How many different twoletter words (including nonsense words) can be formed when
More informationProbability Review 41
Probability Review 41 For the following problems, give the probability to four decimals, or give a fraction, or if necessary, use scientific notation. Use P(A) = 1  P(not A) 1) A coin is tossed 6 times.
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 informationMath June Review: Probability and Voting Procedures
Math  June Review: Probability and Voting Procedures A big box contains 7 chocolate doughnuts and honey doughnuts. A small box contains doughnuts: some are chocolate doughnuts, and the others are honey
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 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 information5.1 Probability Rules
Ch. 5 Probability 5.1 Probability Rules 1 Apply the rules of probabilities. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.
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 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 informationConditional Probability Worksheet
Conditional Probability Worksheet EXAMPLE 4. Drug Testing and Conditional Probability Suppose that a company claims it has a test that is 95% effective in determining whether an athlete is using a steroid.
More 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 Questions on Ch4 and Ch5
Review Questions on Ch4 and Ch5 1. Find the mean of the distribution shown. x 1 2 P(x) 0.40 0.60 A) 1.60 B) 0.87 C) 1.33 D) 1.09 2. A married couple has three children, find the probability they are all
More informationChapter 3: Elements of Chance: Probability Methods
Chapter 3: Elements of Chance: Methods Department of Mathematics Izmir University of Economics Week 34 20142015 Introduction In this chapter we will focus on the definitions of random experiment, outcome,
More informationFinite Mathematics MAT 141: Chapter 8 Notes
Finite Mathematics MAT 4: Chapter 8 Notes Counting Principles; More David J. Gisch The Multiplication Principle; Permutations Multiplication Principle Multiplication Principle You can think of the multiplication
More informationCHAPTER 8 Additional Probability Topics
CHAPTER 8 Additional Probability Topics 8.1. Conditional Probability Conditional probability arises in probability experiments when the person performing the experiment is given some extra information
More informationChapter 4: Probability
Student Outcomes for this Chapter Section 4.1: Contingency Tables Students will be able to: Relate Venn diagrams and contingency tables Calculate percentages from a contingency table Calculate and empirical
More informationCS 361: Probability & Statistics
January 31, 2018 CS 361: Probability & Statistics Probability Probability theory Probability Reasoning about uncertain situations with formal models Allows us to compute probabilities Experiments will
More informationExam 2 Review (Sections Covered: 3.1, 3.3, , 7.1) 1. Write a system of linear inequalities that describes the shaded region.
Exam 2 Review (Sections Covered: 3.1, 3.3, 6.16.4, 7.1) 1. Write a system of linear inequalities that describes the shaded region. 5x + 2y 30 x + 2y 12 x 0 y 0 2. Write a system of linear inequalities
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 informationSection : Combinations and Permutations
Section 11.111.2: Combinations and Permutations Diana Pell A construction crew has three members. A team of two must be chosen for a particular job. In how many ways can the team be chosen? How many words
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 information