# 3 The multiplication rule/miscellaneous counting problems

Size: px
Start display at page:

Transcription

1 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, what is P (A B)? What is P (A B)? 2 Permutations and Combinations 2. Roll a die ten times. What the probability of getting exactly four 6 s? (For example, this occurs if you roll ). 3. In tossing 4 fair dice, what s the probability of tossing at most one 3? 4. How many anagrams of MISSISSIPPI are there? 5. The price of a certain stock changes each day at random: it goes up \$1 with probability 0.6 and down \$1 with probability 0.4. Assuming that changes on different days are independent, (a) what s the probability that it will be back to its starting price after 10 days? (b) what s the probability that it will be up by at least \$1 after 4 days? 6. What is the coefficient on x 4 y 6 in the product (2x + 3y) 10? 3 The multiplication rule/miscellaneous counting problems 7. A hand of poker consists of 5 cards randomly drawn from a deck of 52 cards. What s the probability of getting 4-of-a-kind? (There are 13 kinds and 4 suits. Each card has a suit and a kind for a total of 4x13=52 cards). 8. A 5-card hand is dealt from a well-shuffled deck of 52 playing cards. What is the probability that the hand contains at least one card from each of the four suits? 9. You are dealt 6 cards from a standard deck of 52 cards. What is the probability that you get a four-of-a-kind and two cards that don t match. For example, you could get 4 Kings, a 10 and a 3. But you couldn t get 4 Kings and two 10s. 10. A licence plate consists of 3 letters followed by 3 numbers (for example XTY438). If no letter can be used more than once how many licence plates are there? The numbers can be repeated. For example XTY004 is valid.

2 11. In a bridge game, each of 4 players gets 13 cards drawn at random from an ordinary deck of 52 cards. What is the probability that two players each have 2 aces? There are 4 aces in the deck. 12. A certain group of 20 people consists of 7 doctors, 3 lawyers and 10 bankers. They are all seated at random around a round table. (a) What is the probability that the 3 lawyers sit next to each other? (b) What is the probability that no doctor sits next to another doctor? 13. A school play has 4 distinct male roles and 5 distinct female roles. If 7 men and 8 women audition for the play, how many possible casts are there? What if Bob and Alice refuse to be in the play together? 4 Urn problems 14. Urn #1 contains 3 black and 4 red balls. Urn #2 contains 5 black and 2 red balls. A ball is chosen at random from urn #1. A ball is also chosen at random from urn #2. What s the probability the two balls have the same color? 15. An urn contains 100 balls: 25 red, 25 blue, 50 green. Select 12 balls at random from the urn. (a) Assume that the selection is done without replacement. Compute the probability that 3 red, 4 blue ball and 5 green balls are selected. (b) Assume the same question if the selection is done with replacement. (c) What is the probability that all 12 balls have the same color? (assume the selection is done without replacement, then answer the same problem with replacement). (d) An urn contains 10 red balls and 5 blue balls. You grab 4 balls at random (without replacement). What is the probability that you grabbed 2 red balls and 2 black balls? 5 Inclusion/Exclusion and union problems 16. Suppose you draw 8 cards out of a regular deck of 52 cards. What is the probability that you will have at least 6 cards of the same suit? 17. In a certain city, 50% of the people speak Spanish, 45% speak English, 40% speak French, 15% speak Spanish and English, 15% speak English and French, 10% speak Spanish and French. If everyone speaks at least one of these three languages then what percentage of people speak all three? 18. Suppose you are dealt 5 cards at random from an ordinary deck of 52 cards. What s the probability of getting exactly four face cards? A face card is a king, queen or jack. There are 12 face cards in the deck.

5 31. A coin is tossed twice. Consider the events: A = heads on the first toss. B = heads on the second toss. C = the two tosses come out the same. (a) Are A, B independent? (b) Are B, C independent? (c) Are A, C independent? (d) Are A, B, C jointly independent? Justify your answer. 32. Suppose P (A) = 0.2, P (B) = 0.3. (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 P (A B)? What is P (A B)? 33. The price of a certain stock changes each day at random: it goes up \$1 with probability 0.6 and down \$1 with probability 0.4. Assuming that changes on different days are independent, what s the probability that it will be back to its starting price after 10 days?

### 3 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

### 1 2-step 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 2-step and other basic conditional probability problems 1. Suppose A, B, C are

### 1 2-step 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 2-step and other basic conditional probability problems 1. Suppose A, B, C are

### Math 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

### MATH 215 DISCRETE MATHEMATICS INSTRUCTOR: P. WENG

MATH DISCRETE MATHEMATICS INSTRUCTOR: P. WENG Counting and Probability Suggested Problems Basic Counting Skills, Inclusion-Exclusion, and Complement. (a An office building contains 7 floors and has 7 offices

### 1. 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,

### Mathematical Foundations HW 5 By 11:59pm, 12 Dec, 2015

1 Probability Axioms Let A,B,C be three arbitrary events. Find the probability of exactly one of these events occuring. Sample space S: {ABC, AB, AC, BC, A, B, C, }, and S = 8. P(A or B or C) = 3 8. note:

### Chapter 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

### The 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

### 2.5 Sample Spaces Having Equally Likely Outcomes

Sample Spaces Having Equally Likely Outcomes 3 Sample Spaces Having Equally Likely Outcomes Recall that we had a simple example (fair dice) before on equally-likely sample spaces Since they will appear

### Conditional 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.

### (a) Suppose you flip a coin and roll a die. Are the events obtain a head and roll a 5 dependent or independent events?

Unit 6 Probability Name: Date: Hour: Multiplication Rule of Probability By the end of this lesson, you will be able to Understand Independence Use the Multiplication Rule for independent events Independent

### Conditional Probability Worksheet

Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 3-6, compute the conditional probabilities P( AB) and P( B A ) 3. P A = 0.7, P B = 0.4, P A B = 0.25 4. P A = 0.45, P B = 0.8, P A

### Probability. The Bag Model

Probability The Bag Model Imagine a bag (or box) containing balls of various kinds having various colors for example. Assume that a certain fraction p of these balls are of type A. This means N = total

### November 8, Chapter 8: Probability: The Mathematics of Chance

Chapter 8: Probability: The Mathematics of Chance November 8, 2013 Last Time Probability Models and Rules Discrete Probability Models Equally Likely Outcomes Crystallographic notation The first symbol

### Probability 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

### The 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

### Key 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

### Contents 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

### The 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

### Pan (7:30am) Juan (8:30am) Juan (9:30am) Allison (10:30am) Allison (11:30am) Mike L. (12:30pm) Mike C. (1:30pm) Grant (2:30pm)

STAT 225 FALL 2012 EXAM ONE NAME Your Section (circle one): Pan (7:30am) Juan (8:30am) Juan (9:30am) Allison (10:30am) Allison (11:30am) Mike L. (12:30pm) Mike C. (1:30pm) Grant (2:30pm) Grant (3:30pm)

### TEST 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

### PROBABILITY. 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

### MULTIPLE 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

### Unit 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

### Dependence. Math Circle. October 15, 2016

Dependence Math Circle October 15, 2016 1 Warm up games 1. Flip a coin and take it if the side of coin facing the table is a head. Otherwise, you will need to pay one. Will you play the game? Why? 2. If

### The probability set-up

CHAPTER The probability set-up.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

### Independent 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

### Intermediate 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.

### 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

### Here are two situations involving chance:

Obstacle Courses 1. Introduction. Here are two situations involving chance: (i) Someone rolls a die three times. (People usually roll dice in pairs, so dice is more common than die, the singular form.)

### November 11, Chapter 8: Probability: The Mathematics of Chance

Chapter 8: Probability: The Mathematics of Chance November 11, 2013 Last Time Probability Models and Rules Discrete Probability Models Equally Likely Outcomes Probability Rules Probability Rules Rule 1.

### Chapter 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.

### 7.1 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

### Probability --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..

### 6) 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

### A Probability Work Sheet

A Probability Work Sheet October 19, 2006 Introduction: Rolling a Die Suppose Geoff is given a fair six-sided die, which he rolls. What are the chances he rolls a six? In order to solve this problem, we

### Section 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

### Section : Combinations and Permutations

Section 11.1-11.2: 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

### CS1800: Intro to Probability. Professor Kevin Gold

CS1800: Intro to Probability Professor Kevin Gold Probability Deals Rationally With an Uncertain World Using probabilities is the only rational way to deal with uncertainty De Finetti: If you disagree,

### STAT Statistics I Midterm Exam One. Good Luck!

STAT 515 - Statistics I Midterm Exam One Name: Instruction: You can use a calculator that has no connection to the Internet. Books, notes, cellphones, and computers are NOT allowed in the test. There are

### Class 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:

### Normal Distribution Lecture Notes Continued

Normal Distribution Lecture Notes Continued 1. Two Outcome Situations Situation: Two outcomes (for against; heads tails; yes no) p = percent in favor q = percent opposed Written as decimals p + q = 1 Why?

### Chapter 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

### Chapter-wise 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

### Unit 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

### Such 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

### Name Instructor: Uli Walther

Name Instructor: Uli Walther Math 416 Fall 2016 Practice Exam Questions You are not allowed to use books or notes. Calculators are permitted. Full credit is given for complete correct solutions. Please

### AP Statistics Ch In-Class Practice (Probability)

AP Statistics Ch 14-15 In-Class Practice (Probability) #1a) A batter who had failed to get a hit in seven consecutive times at bat then hits a game-winning home run. When talking to reporters afterward,

### Unit 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

### Section 5.4 Permutations and Combinations

Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to

### { a, b }, { a, c }, { b, c }

12 d.) 0(5.5) c.) 0(5,0) h.) 0(7,1) a.) 0(6,3) 3.) Simplify the following combinations. PROBLEMS: C(n,k)= the number of combinations of n distinct objects taken k at a time is COMBINATION RULE It can easily

### MULTIPLE 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

### Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results:

Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results: Outcome Frequency 1 8 2 8 3 12 4 7 5 15 8 7 8 8 13 9 9 10 12 (a) What is the experimental probability

### Total. 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

### I. 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

### Counting (Enumerative Combinatorics) X. Zhang, Fordham Univ.

Counting (Enumerative Combinatorics) X. Zhang, Fordham Univ. 1 Chance of winning?! What s the chances of winning New York Megamillion Jackpot!! just pick 5 numbers from 1 to 56, plus a mega ball number

### CISC 1400 Discrete Structures

CISC 1400 Discrete Structures Chapter 6 Counting CISC1400 Yanjun Li 1 1 New York Lottery New York Mega-million Jackpot Pick 5 numbers from 1 56, plus a mega ball number from 1 46, you could win biggest

### Section 5.4 Permutations and Combinations

Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! = n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to

### 4.3 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:

### Chapter 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.

### Chapter 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

### Probability 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.

### MA151 Chapter 4 Section 3 Worksheet

MA151 Chapter 4 Section 3 Worksheet 1. State which events are independent and which are dependent. a. Tossing a coin and drawing a card from a deck b. Drawing a ball from an urn, not replacing it and then

### CSE 312: Foundations of Computing II Quiz Section #2: Inclusion-Exclusion, Pigeonhole, Introduction to Probability (solutions)

CSE 31: Foundations of Computing II Quiz Section #: Inclusion-Exclusion, Pigeonhole, Introduction to Probability (solutions) Review: Main Theorems and Concepts Binomial Theorem: x, y R, n N: (x + y) n

### Contemporary 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 13-15 Time Limit: 90 Minutes No Scratch Paper Calculator Allowed: Scientific Name: The point value of each problem is in the left-hand margin.

### MTH 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)

### Section 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

### Chapter 3: Elements of Chance: Probability Methods

Chapter 3: Elements of Chance: Methods Department of Mathematics Izmir University of Economics Week 3-4 2014-2015 Introduction In this chapter we will focus on the definitions of random experiment, outcome,

### 6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices?

Pre-Calculus Section 4.1 Multiplication, Addition, and Complement 1. Evaluate each of the following: a. 5! b. 6! c. 7! d. 0! 2. Evaluate each of the following: a. 10! b. 20! 9! 18! 3. In how many different

### Week 1: Probability models and counting

Week 1: Probability models and counting Part 1: Probability model Probability theory is the mathematical toolbox to describe phenomena or experiments where randomness occur. To have a probability model

### Chapter 2. Permutations and Combinations

2. Permutations and Combinations Chapter 2. Permutations and Combinations In this chapter, we define sets and count the objects in them. Example Let S be the set of students in this classroom today. Find

### CHAPTERS 14 & 15 PROBABILITY STAT 203

CHAPTERS 14 & 15 PROBABILITY STAT 203 Where this fits in 2 Up to now, we ve mostly discussed how to handle data (descriptive statistics) and how to collect data. Regression has been the only form of statistical

### November 6, Chapter 8: Probability: The Mathematics of Chance

Chapter 8: Probability: The Mathematics of Chance November 6, 2013 Last Time Crystallographic notation Groups Crystallographic notation The first symbol is always a p, which indicates that the pattern

### RANDOM EXPERIMENTS AND EVENTS

Random Experiments and Events 18 RANDOM EXPERIMENTS AND EVENTS In day-to-day 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

### Name: 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

### Chapter 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

### STAT 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

### Probability and Randomness. Day 1

Probability and Randomness Day 1 Randomness and Probability The mathematics of chance is called. The probability of any outcome of a chance process is a number between that describes the proportion of

### Chapter 5: Probability: What are the Chances? Section 5.2 Probability Rules

+ Chapter 5: Probability: What are the Chances? Section 5.2 + Two-Way Tables and Probability When finding probabilities involving two events, a two-way table can display the sample space in a way that

### Exam 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

### Classical 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

### Grade 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.

### Chapter 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

### STAT 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

### Statistics Intermediate Probability

Session 6 oscardavid.barrerarodriguez@sciencespo.fr April 3, 2018 and Sampling from a Population Outline 1 The Monty Hall Paradox Some Concepts: Event Algebra Axioms and Things About that are True Counting

### Most 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:

### Chapter 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

### MULTIPLE 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

### CHAPTER 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

### Section 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

### MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE

MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING 2009 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the

### MULTIPLE 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

### PROBABILITY Case of cards

WORKSHEET NO--1 PROBABILITY Case of cards WORKSHEET NO--2 Case of two die Case of coins WORKSHEET NO--3 1) Fill in the blanks: A. The probability of an impossible event is B. The probability of a sure

### Probability. 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

### Simulations. 1 The Concept

Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that can be

### Math 166: Topics in Contemporary Mathematics II

Math 166: Topics in Contemporary Mathematics II Xin Ma Texas A&M University September 30, 2017 Xin Ma (TAMU) Math 166 September 30, 2017 1 / 11 Last Time Factorials For any natural number n, we define