North Seattle Community College Winter ELEMENTARY STATISTICS 2617 MATH Section 05, Practice Questions for Test 2 Chapter 3 and 4
|
|
- Cecil West
- 6 years ago
- Views:
Transcription
1 North Seattle Community College Winter 2012 ELEMENTARY STATISTICS 2617 MATH Section 05, Practice Questions for Test 2 Chapter 3 and 4 1. Classify each statement as an example of empirical probability, classical probability, or subjective probability. i) The probability a randomly selected citizen will approve of the U. S. President is Empirical since presidential approval rates are based on surveys. ii) The probability a child will attend the same college as his father is 0.4. Empirical if the probability is based on a historical study. Subjective if it based on intuition or educated guess. iii) The probability of rolling an even number on a six-sided die is 0.5. Classical 2. A probability experiment consists of picking one marble from a box that contains a red, a yellow, and a blue marble, and then flipping a coin once. Identify the sample space. (Let R = red, Y = yellow, B = blue, H = head, and T = tail.) Sample space={rh, RT, YH, YT, BH, BT} 3. Suppose that only three types of birds frequent your neighborhood and for a four-hour period, you record the birds you observe flying into your backyard. During that time, you observe 19 cardinals, 16 blue jays, and 12 robins. If each bird is equally likely to fly into your backyard, what is the probability that the next bird you observe is a robin? #!"!"#$%&!"#$%&!!!"#$!!"#$%"&' P(robin) = =!" = #!"!"#$%!"#$%&!!!"#$!!"#$%"&'!"!!"!!" 4. If 15% of the population is left-handed, what is the probability that in a randomly selected group of five people, all five people are left-handed? This is a binomial distribution where n=5, p=0.15, q=.85, x=5 P(x=5) = 5C 5(0.15) 5 (0.85) 0 = A multiple-choice test has three questions, each with four choices for the answer, of which only one of the choices is correct. What is the probability of guessing correctly on at least one of the questions? This is a binomial distribution where n=3, p=0.25, q=.75, x=0,1,2,3 1-P(x=0) =1-3C 0(0.25) 0 (0.75) 3 = Suppose a traffic light cycles where it is green for 180 seconds, then yellow for 10 seconds, and then red for 110 seconds. Find the probability that at a certain time the light is green. P(green) = 180/( ) = 0.6
2 7. One card is randomly picked from a deck of playing cards. What is the probability that a face card was picked, given it was not a king or a heart? #!"!"#$!"#$%!"#$%! A={face} B={not king or not heart}, we need to find P(A B)= #!"!"#$%!"#$%! # of cards given B = # of cards that are neither king or hearts is = = 36 # of face cards given b = # (queens and jacks that are not hearts) = 6 P(A B) = 6/36 =1/6 8. Use the following information to answer questions 8 and 9. A random sample of 250 students are classified by type of school and reading ability. What is the probability of randomly picking a student with average reading ability, given the student attends a private school? P(average private school) = 47/( ) = Classify the events of picking a student with an average reading ability and picking a student from a private school as mutually exclusive or not mutually exclusive and as independent or dependent. A = {average} B = {private school} P(A and B) =!" 0 therefore they are not mutually exclusive events ( i.e. there are students!"# who are private schooled with average reading ability) P(A B) =!"!"# P(B) = therefore they are dependent (i.e. whether a student will be average!"#!"# has some dependence on whether a student goes to private or public school) 10. Two cards are randomly selected, without replacement, from a standard deck of playing cards. What is the probability of first picking a five and then picking a card other than a five? P(1 st pick 5 and 2 nd pick not 5) = P(1 st pick 5) * P(2 nd pick not 5/1 st pick is 5) = (4/52)(48/51) = 192/2652 = If two six-sided dice are rolled once, what is the probability of rolling doubles (same number on each die) and a sum of six? Only possibility is (3,3), therefore the associated probability is P(A and B) = P(A/B) * P(B) = P(A) * P(B) [since the two rolls are independent of each either] = (1/6)(1/6) = 1/36 = If two six-sided dice are rolled once, what is the probability of rolling doubles or a sum of six? A = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)} B= {(1,5),(5,1),(2,4),(4,2),(3,3)} P(A or B) = P(A) + P(B) P(A and B) = (6/36) + (5/36) (1/36) = 0.278
3 13. A network executive has to decide on the programming line-up for Thursday night. If there are ten shows to choose from, how many six-show line-ups are possible? 10C 6 =10!/(6! (10-6)!) = How many license plates are possible if they consist of three letters followed by three digits? Repetition is permitted. 26*26*26*10*10*10=17,576, When you buy a one-dollar ticket for the Florida Lotto, you are trying to match six numbers drawn from 53 numbers, in any order. How many different tickets are possible? 53C 6 =53!/(6! (53-6)!) = 22,957, Decide if the following events are mutually exclusive and whether or not they are independent or dependent. Event A: drawing a queen from a standard deck of 52 cards Event B: drawing a heart or diamond from a standard deck of 52 cards Not Mutually Exclusive (Queen Hearts for example) Independent (either draw is from a deck of 52 cards which implies the cards are replaced back into the deck) 17. A local bicycle shop is holding a raffle in which 5 bicycles will be given away. 500 tickets will be sold, 5 of which are winners. If you buy 10 tickets, in how many ways can you not win a bicycle? Not winning implies you pick from the losing set of 495 tickets therefore the required event is 495C 10 = 222,102,077,451,647,000, If there are 30 entries in a best of breed dog show, in how many ways can 1 st, 2 nd and 3 rd place be awarded? 30P 3= In questions 19 and 20, the table shows the number of traffic violations by day of occurrence and type of offense for a particular city. Use the table to find the indicated probabilities. A traffic violation is randomly selected. What is the probability that it is a speeding violation? P(speed violation) = 245/924 = 0.265
4 20. A traffic violation is randomly selected. What is the probability that it is a speeding violation given that the violation occurred on a weekend? P(speed violation weekend) = 69/238 = In questions 21 and 22, the table shows the number of injuries sustained over the course of a season by football players in a particular conference according to position and side (offense/defense). Use the table to find the indicated probabilities. An injured player is randomly chosen. What is the probability that the player was a back or an offensive player? P(Backs or Offensive) = P(Backs) + P(Offensive) P(Backs and Offensive) = 42/ /126 18/126 = 90/126 = An injured player is randomly chosen. What is the probability that the player was not a lineman given that he played defense? P(not Lineman Defensive) = P(not Linemen and Defensive)/P(Defensive) = ((24+12)/126)/(60/126) = A sandwich shop offers three different breads, five different meats and four different cheeses. How many sandwich combinations involving exactly one of each bread, meat and cheese does the shop offer? 3*5*4= A six-sided die is rolled once and the outcome is observed. Define the events A and B as follows: Event A: Number observed is even Event B: Number observed is greater than 3 Find P(A or B). P(A or B) = P(A) + P(B) - P(A and B) = (3/6) + (3/6) (2/6) = 4/6 = 2/3 25. Decide if the random variables defined below are discrete or continuous. i) x represents the word count of each editorial printed in the New York Times. ii) x represents the time it takes a pizza delivery man to deliver an order. iii) the number of quarterbacks currently playing in the NFL iv) the current ages of the quarterbacks Discrete, Continuous, Discrete, Discrete 26. Identify the random variable x here and calculate P(x) for the data given in the following table.
5 Also compute mean, variance, standard deviation and expected value of x. (I am treating >=3 as 3 here) Cars Household P(x) xp(x) (x-µ) (x-µ) 2 P(x) μ =2.14 σ 2 =0.57 Mean, μ = 2.14 Variance, σ! = 0.57 Standard deviation, σ = Which of the following relative frequency histograms best represents the probability distribution for the data given in the table below? a) b)
6 c) d) Answer: d) 28. Calculate the mean and variance of the probability distribution described in the following table.
7 X P(x) xp(x) (x-µ) (x-µ) 2 P(x) Mean = 2.86 Variance = 1.50 Standard Deviation = The table given below lists the number of widows on welfare based on the number of dependent children in the household for a particular city. Find the probability that a widow selected at random has no more than three children. P(# of children 3) = ( )/( ) 30. For questions 30, 31 and 32, assume that at a game at the town fair contestants win 15% of the times. A player plays the game 15 times. What is the mean and variance for the number of wins? This is a binomial distribution n=15, p=0.15, x= 0,1,2,,15 Mean = np = 15*0.15 =2.25 Variance=npq = 15*0.15*0.85 = What is the probability that the player wins at least 3 times? P(x 3) = 1-P(x<2) = 1-P(x=0)-P(x=1)-P(x=2) = ! 0.85!" = = ! 0.85!" ! 0.85!" 32. Given the following is a probability distribution of a random variable, x, determine P(x = 3). P(x=3) = 0.23
8 34. The discrete random variable, x, is the number of students absent from class, and f is the number of classes. Determine which of the following options below represents the probability distribution associated with x where x = 0, 1, 2, 3, 4. (a) 0.06, 0.16, 0.12, 0.08, 0.07 (b) 0, 0.06, 0.17, 0.08, 0.49 (c) 0, 0.25, 0.50, 0.75, 1 (d) 0.14, 0.32, 0.24, 0.16, 0.14 (d) since all values add up to 1 and each value lies between 0 and 1 both inclusive 35. There are ten marbles in a box: one red, three yellow, and six bl.ue. You are given one pick from the box for 75 cents. You win $5 if you pick a red marble, $1 if you pick a yellow marble, and nothing if you pick a blue marble. If you play the game once, what is your expected net gain? Color of ball Gain Frequency P(x) xp(x) Red Yellow Blue Mean, µ = If you play the game described in question 35 one time, what is the probability that you win (not net) at least one dollar? P(red or yellow) = P(win 5 or win 1) = P(win 5) + P(win 1) = = Find the probability of having exactly four girls in seven births. Assume no multiple births and that male and female births are equally likely and independent. This is a binomial distribution with n=7 trials, probability of success, p=0.5, probability of failure, q=0.5 and x can take any of the following values - 0,1,2,3,4,5,6,7 P(x=4) = 7C 4(0.5) 4 (0.5) 3 = Research shows that 72% of consumers have heard of MBI computers. A survey of 500 randomly selected consumers is to be conducted. What is the mean and standard deviation for the number of consumers that have heard of MBI computers? This is a binomial distribution with n=500, p=0.72, q=0.28, x=0,1,2,,500 Mean = np = 360 Standard Deviation = npq = = 10.04
9 39. Suppose that 20% of the M & M s made by Mars, Inc. are red. What is the probability that in a sample of 50 randomly selected M & M s, exactly 15 are red? This is a binomial distribution with n=50, p=0.20, q=0.80, x=0,1,2,,50 P(x=50) = = 50C 15(0.5) 15 (0.5) 35 = If events A and B are independent and P(A) = 0.6 and P(B) = 0.3 then what P(A and B) isp(a and B) = P(A)P(B) = 0.18 when independent 41. If P(A) = 0.5, P(B) = 0.6, and P(A and B) = 0.3 then compute P(A or B) is P(A or B) = P(A) + P(B) P(A and B) = = If P(A) = 0.6, P(B) = 0.5, and P(A or B) = 0.9, then P(A and B) is P(A and B) = P(A) + P(B) P(A or B) = = If P(A) = 0.3, P(B) = 0.5, and P(A or B) = 0.6, then P(A B) is P(A B) = P(A and B)/P(B) = (P(A) + P(B) P(A or B))/P(B) = 0.2/0.5 = If P(A) = 0.5, P(B) = 0.4, and P(B A) = 0.3, then P(A and B) is P(A and B)=P(B A) * P(A) =0.3*0.5= If A and B are independent events and P(A) = 0.3 and P(B) = 0.6, then P(A or B) is P(A and B) = 0, P(A or B) = P(A) + P(B) = If A and B are mutually exclusive events and P(A) = 0.3 and P(B) = 0.6, then P(A and B) is P(A and B) = Given that events A and B are mutually exclusive, a) P(A or B) = P(A and B) b) P(A or B) = P(A) + P(B) - P(A)P(B) c) P(A or B) = P(A) + P(B) d) P(A or B) = P(A) + P(B) - P(A and B) Answer: c) 48. If P(A) = 0.6, P(B) = 0.3, and P(A B) = 0.4, then P(A') (i.e. the probability of A complement) is? P(A')=1-P(A)=1-0.6= The probability that any one of two engines on an aircraft will not fail is Assuming that both engines operate independently of each other what is the probability that both engines will not fail? P(E1 works) = P(E2 work) = P(E1 works and E2 works) = P(E1) * P(E2) = 0.998
10 50. If two events cannot occur at the same time, then these two events are a) independent b) conditional c) simple d) mutually exclusive Answer =d) 51. If A and B are two mutually exclusive events with P(A) = 0.15 and P(B) = 0.4, then what is P(A and B') (i.e. probability of A and B complement)? P(A and B')=P(A).P(B'/A) = P(A).(1-P(B A))= P(A)(1-P(B)) =P(A) P(A)P(B) = P(A) = If two nontrivial events (probability not equal to zero) A and B are mutually exclusive, which of the following must be true? a) P(A or B) = P(A)P(B) b) P(A and B) = P(A)P(B) c) P(A or B) = P(A) + P(B) d) P(A and B) = P(A) + P(B) Answer = c) 53. How many different four letter words can be formed (the words need not be meaningful) using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R? The 1 st letter is E the last letter is R, therefore, one has to find two letters from the remaining 11. Of the 11 letters, there are 2 Ns, 2Es, 2As, 1M, 1R, 1D, 1T and 1I. The second and third positions can either have two different letters or have both the letters to be the same. Case 1: When the two letters are different. One has to choose two different letters from the 8 remaining choices. This can be done is 8*7 ways = 56 ways. Case 2: When the two letters are same. There are 3 options the three letters can be either Ns or Es or As. Therefore, 3 ways. Total number of possibilities = = There are five women and six men in a group. From this group a committee of 4 is to be chosen. (a) How many different ways can a committee be formed that contain three women and one man? 5C 3* 6C 1=60 ways (b) What is the probability of forming a committee with three women and one man? P(3 women and 1 man) = 5C 3* 6C 1/ 11C 4 =0.182 (c) How many different ways can a committee be formed that contains at least three women? Event(atleast 3 women) = Event(3 women and 1 man) + Event(4 women)= 5C 3* 6C 1 + 5C 4=65 ways (d) What is the probability of forming a committee with atleast three women. P(atleast 3 women) = P(3 women and 1 man) + P(4 women) = ( 5C 3* 6C 1/ 11C 4 )+( 5C 4/ 11C 4) = = 0.197
4.1 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 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 Week-in-Reviews
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 informationMath 1342 Exam 2 Review
Math 1342 Exam 2 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) If a sportscaster makes an educated guess as to how well a team will do this
More informationThe point value of each problem is in the left-hand 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 5-7 4 Problem Pages 4 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of
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 informationMath Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.
Math 166 Fall 2008 c Heather Ramsey Page 1 Math 166 - Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 3.2 - Measures of Central Tendency
More informationMath Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.
Math 166 Fall 2008 c Heather Ramsey Page 1 Math 166 - Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 3.2 - Measures of Central Tendency
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 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 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 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 informationMath 141 Exam 3 Review with Key. 1. P(E)=0.5, P(F)=0.6 P(E F)=0.9 Find ) b) P( E F ) c) P( E F )
Math 141 Exam 3 Review with Key 1. P(E)=0.5, P(F)=0.6 P(E F)=0.9 Find C C C a) P( E F) ) b) P( E F ) c) P( E F ) 2. A fair coin is tossed times and the sequence of heads and tails is recorded. Find a)
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 informationChapter 8: Probability: The Mathematics of Chance
Chapter 8: Probability: The Mathematics of Chance Free-Response 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 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 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 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 3-1 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 informationChapter 1: Sets and Probability
Chapter 1: Sets and Probability Section 1.3-1.5 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 informationThe Teachers Circle Mar. 20, 2012 HOW TO GAMBLE IF YOU MUST (I ll bet you $5 that if you give me $10, I ll give you $20.)
The Teachers Circle Mar. 2, 22 HOW TO GAMBLE IF YOU MUST (I ll bet you $ that if you give me $, I ll give you $2.) Instructor: Paul Zeitz (zeitzp@usfca.edu) Basic Laws and Definitions of Probability If
More 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 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 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 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 informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1342 Practice Test 2 Ch 4 & 5 Name 1) Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. 1) List the outcomes
More informationMath 1 Unit 4 Mid-Unit Review Chances of Winning
Math 1 Unit 4 Mid-Unit Review Chances of Winning Name My child studied for the Unit 4 Mid-Unit Test. I am aware that tests are worth 40% of my child s grade. Parent Signature MM1D1 a. Apply the addition
More informationAdvanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY
Advanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY 1. Jack and Jill do not like washing dishes. They decide to use a random method to select whose turn it is. They put some red and blue
More informationChapter 4: Probability and Counting Rules
Chapter 4: Probability and Counting Rules Before we can move from descriptive statistics to inferential statistics, we need to have some understanding of probability: Ch4: Probability and Counting Rules
More informationDiscrete Random Variables Day 1
Discrete Random Variables Day 1 What is a Random Variable? Every probability problem is equivalent to drawing something from a bag (perhaps more than once) Like Flipping a coin 3 times is equivalent to
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.
4-1 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 Introduction to Sets
Section 1.1 - Introduction to Sets Definition: A set is a well-defined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase
More informationTotal. STAT/MATH 394 A - Autumn Quarter Midterm. Name: Student ID Number: Directions. Complete all questions.
STAT/MATH 9 A - Autumn Quarter 015 - Midterm Name: Student ID Number: Problem 1 5 Total Points Directions. Complete all questions. You may use a scientific calculator during this examination; graphing
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 informationKey Concepts. Theoretical Probability. Terminology. Lesson 11-1
Key Concepts Theoretical Probability Lesson - Objective Teach students the terminology used in probability theory, and how to make calculations pertaining to experiments where all outcomes are equally
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) 1 6
Math 300 Exam 4 Review (Chapter 11) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give the probability that the spinner shown would land on
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 informationProbability Concepts and Counting Rules
Probability Concepts and Counting Rules Chapter 4 McGraw-Hill/Irwin Dr. Ateq Ahmed Al-Ghamedi Department of Statistics P O Box 80203 King Abdulaziz University Jeddah 21589, Saudi Arabia ateq@kau.edu.sa
More informationAlgebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations
Algebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations Objective(s): Vocabulary: I. Fundamental Counting Principle: Two Events: Three or more Events: II. Permutation: (top of p. 684)
More informationFundamental. If one event can occur m ways and another event can occur n ways, then the number of ways both events can occur is:.
12.1 The Fundamental Counting Principle and Permutations Objectives 1. Use the fundamental counting principle to count the number of ways an event can happen. 2. Use the permutations to count the number
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 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 informationS = {(1, 1), (1, 2),, (6, 6)}
Part, MULTIPLE CHOICE, 5 Points Each An experiment consists of rolling a pair of dice and observing the uppermost faces. The sample space for this experiment consists of 6 outcomes listed as pairs of numbers:
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 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 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 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 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 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 informationBefore giving a formal definition of probability, we explain some terms related to probability.
probability 22 INTRODUCTION In our day-to-day life, we come across statements such as: (i) It may rain today. (ii) Probably Rajesh will top his class. (iii) I doubt she will pass the test. (iv) It is unlikely
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 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 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 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the
More informationSuch a description is the basis for a probability model. Here is the basic vocabulary we use.
5.2.1 Probability Models When we toss a coin, we can t know the outcome in advance. What do we know? We are willing to say that the outcome will be either heads or tails. We believe that each of these
More informationChapter 3: Probability (Part 1)
Chapter 3: Probability (Part 1) 3.1: Basic Concepts of Probability and Counting Types of Probability There are at least three different types of probability Subjective Probability is found through people
More informationHonors Precalculus Chapter 9 Summary Basic Combinatorics
Honors Precalculus Chapter 9 Summary Basic Combinatorics A. Factorial: n! means 0! = Why? B. Counting principle: 1. How many different ways can a license plate be formed a) if 7 letters are used and each
More informationTextbook: pp Chapter 2: Probability Concepts and Applications
1 Textbook: pp. 39-80 Chapter 2: Probability Concepts and Applications 2 Learning Objectives After completing this chapter, students will be able to: Understand the basic foundations of probability analysis.
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 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 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 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 information1. Determine whether the following experiments are binomial.
Math 141 Exam 3 Review Problem Set Note: Not every topic is covered in this review. It is more heavily weighted on 8.4-8.6. Please also take a look at the previous Week in Reviews for more practice problems
More information6) A) both; happy B) neither; not happy C) one; happy D) one; not happy
MATH 00 -- PRACTICE TEST 2 Millersville University, Spring 202 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all natural
More informationFor question 1 n = 5, we let the random variable (Y) represent the number out of 5 who get a heart attack, p =.3, q =.7 5
1 Math 321 Lab #4 Note: answers may vary slightly due to rounding. 1. Big Grack s used car dealership reports that the probabilities of selling 1,2,3,4, and 5 cars in one week are 0.256, 0.239, 0.259,
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 informationMATH 2000 TEST PRACTICE 2
MATH 2000 TEST PRACTICE 2 1. Maggie watched 100 cars drive by her window and compiled the following data: Model Number Ford 23 Toyota 25 GM 18 Chrysler 17 Honda 17 What is the empirical probability that
More informationCSC/MTH 231 Discrete Structures II Spring, Homework 5
CSC/MTH 231 Discrete Structures II Spring, 2010 Homework 5 Name 1. A six sided die D (with sides numbered 1, 2, 3, 4, 5, 6) is thrown once. a. What is the probability that a 3 is thrown? b. What is the
More information4.1 What is Probability?
4.1 What is Probability? between 0 and 1 to indicate the likelihood of an event. We use event is to occur. 1 use three major methods: 1) Intuition 3) Equally Likely Outcomes Intuition - prediction based
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 information13-6 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 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 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 informationM146 - Chapter 5 Handouts. Chapter 5
Chapter 5 Objectives of chapter: Understand probability values. Know how to determine probability values. Use rules of counting. Section 5-1 Probability Rules What is probability? It s the of the occurrence
More informationThe probability set-up
CHAPTER 2 The probability set-up 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 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 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 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 two-letter words (including nonsense words) can be formed when
More informationChapter 5 - Elementary Probability Theory
Chapter 5 - Elementary Probability Theory Historical Background Much of the early work in probability concerned games and gambling. One of the first to apply probability to matters other than gambling
More information1MA01: Probability. Sinéad Ryan. November 12, 2013 TCD
1MA01: Probability Sinéad Ryan TCD November 12, 2013 Definitions and Notation EVENT: a set possible outcomes of an experiment. Eg flipping a coin is the experiment, landing on heads is the event If an
More informationSpring 2016 Math 54 Test #2 Name: Write your work neatly. You may use TI calculator and formula sheet. Total points: 103
Spring 2016 Math 54 Test #2 Name: Write your work neatly. You may use TI calculator and formula sheet. Total points: 103 1. (8) The following are amounts of time (minutes) spent on hygiene and grooming
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 informationCHAPTER 7 Probability
CHAPTER 7 Probability 7.1. Sets A set is a well-defined 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 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 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 informationUnit 6: Probability. Marius Ionescu 10/06/2011. Marius Ionescu () Unit 6: Probability 10/06/ / 22
Unit 6: Probability Marius Ionescu 10/06/2011 Marius Ionescu () Unit 6: Probability 10/06/2011 1 / 22 Chapter 13: What is a probability Denition The probability that an event happens is the percentage
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 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 informationTest 2 SOLUTIONS (Chapters 5 7)
Test 2 SOLUTIONS (Chapters 5 7) 10 1. I have been sitting at my desk rolling a six-sided die (singular of dice), and counting how many times I rolled a 6. For example, after my first roll, I had rolled
More informationUnit 6: Probability. Marius Ionescu 10/06/2011. Marius Ionescu () Unit 6: Probability 10/06/ / 22
Unit 6: Probability Marius Ionescu 10/06/2011 Marius Ionescu () Unit 6: Probability 10/06/2011 1 / 22 Chapter 13: What is a probability Denition The probability that an event happens is the percentage
More informationCHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY
CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many real-world fields, such as insurance, medical research, law enforcement, and political science. Objectives:
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 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 informationSection 6.1 #16. Question: What is the probability that a five-card poker hand contains a flush, that is, five cards of the same suit?
Section 6.1 #16 What is the probability that a five-card poker hand contains a flush, that is, five cards of the same suit? page 1 Section 6.1 #38 Two events E 1 and E 2 are called independent if p(e 1
More informationSALES AND MARKETING Department MATHEMATICS. Combinatorics and probabilities. Tutorials and exercises
SALES AND MARKETING Department MATHEMATICS 2 nd Semester Combinatorics and probabilities Tutorials and exercises Online document : http://jff-dut-tc.weebly.com section DUT Maths S2 IUT de Saint-Etienne
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 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 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 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 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 information