# Math 210 Lecture Notes: Ten Probability Review Problems

Save this PDF as:

Size: px
Start display at page:

Download "Math 210 Lecture Notes: Ten Probability Review Problems"

## Transcription

1 Math 210 Lecture Notes: Ten Probability Review Problems Richard Blecksmith Dept. of Mathematical Sciences Northern Illinois University 1. Review Question 1 Face card means jack, queen, or king. You draw two cards from a standard 52 card deck. Find the probability that the first card is not a face card the second card is not a face card given that the first card is not a face card both cards are not face cards at least one of the cards is a face card. Find the probability that 2. Question 1 Solution the first card is not a face card = = the second card is not a face card given that the first card is not a face card = = Question 1 Solution Cont Find the probability that 1

2 2 both cards are not face cards P(both are not face cards)= P(first card not face) P(second card not face first card not face) = = at least one of the cards is a face card. P(at least one face card) = 1 P(both are not face cards) = = Review Question 2 A quarter, a dime, and two nickels are placed in a box. Coins are drawn out one at a time. The drawing continues until a coin is drawn which is of smaller value than the one just previously drawn, or until all the coins are drawn. What is the probability that all four coins will be drawn? ր D Q N 1 ց N 2 ր N 1 ր D N 1 ց N 2 ր D Q N 2 ր ր Q N 2 N 1 D N 2 ց ր Q D N 2 D Q 5. Question 2 Solution Reverse N 1 and N 2 in third branch. P(completion) = 6 24 = Review Question 3 An urn contains seven red and three green balls. A second urn contains five red and five green balls.

3 3 A ball is selected at random from the first urn and placed in the second. Then a ball is selected at random from the second urn. What is the probability of drawing a green ball the first time and a red ball the second time? 7. Question 3 Solution Urn 1: seven red and three green balls. Urn 2: five red and five green balls. A ball is selected at random from Urn 1 and placed in Urn 2. Then a ball is selected from Urn 2. P(first ball green and second ball is red) = P(first ball green) P(second ball is red first ball green) = = Review Question 4 The probability of any particular used marker being good(that is, it actually writes clearly on the board) is 15%. Seven used markers are in a tray by the whiteboard. What is the probability that exactly two of these seven markers are good? 9. Question 4 Solution By the Binomial Distribution Theorem, P(exactly 2 out of 7 is good) = C(7,2)(0.15) 2 (0.85) 5 =.20965

4 4 10. Review Question 5 A bag contains 5 green and 8 red balls. A man is condemned to draw a ball and to be executed if it is red one. The sentence is subsequently mitigated in that the concemned man is now allowed to divide the balls between two bags according to his own preference. He is then blindfolded and made to choose one of the bags and then draw a ball from it. What is, from his point of view, the most favorable division of the balls? 11. Question 5 Solution A bag contains 5 green and 8 red balls. The condemned man should divide the balls into two bags as follows: Bag 1: 1 green ball Bag 2: 4 green, 8 red balls 12. Review Question 6 Events A and B occur with the probabilities: Find P(A) = P(B) = P(A B) P(A B c ) P(A B) Are A and B independent events? P(A B) = 2 11

5 5 P(A) = P(B) = Question 6 Solution P(A B) = 2 11 P(A B) = P(A)+P(B) P(A B) = P(A B c ) = P(A) P(A B) = P(A B) = P(A B) P(B) = 2/11 13/59 = = Are A and B independent events? No P(A B) = P(A) = Review Question 7 In a survey, 60 Catholics and 40 Protestants were asked whether they believe in abortion. Five-twelvths of the Catholics said yes, while 15 of the Protestants said yes. What is the probability that a person picked at random from the survey said yes? If you already know the person responded yes, k what it the probability that he or she is a Catholic? 15. Review Question 7 60 Catholics and 40 Protestants surveyed. 100 = people in the survey. Five-twelvths of the Catholics said yes 5 60 = P(apersonpickedatrandomfromthesurveysaid yes? ) = =

6 6 P(person is Catholic given that the person responded yes ) = = Review Question 8 Among the numbers 1, 2, 3, 4, we first choose one at random; among the remaining numbers we then choose another. Calculate the probability of picking an odd number at the first draw at the second draw at both draws. First number chosen from 1, 2, 3, Question 8 Solution Second number chosen from the remaining 3 numbers. P(first number is odd) 2 4 = 1 2 P(second number is odd) 2 4 = 1 2 Time Out! Maybe you are thinking that the selection of the second ball should be from 3 balls, not 4. So why is the denominator 4? 18. Question 8 Solution Cont d In asking What is the probability the second ball is odd? no conditions are given on the first ball, This question does not ask What is the probability the second ball is odd given that the first ball is odd. Without conditions there is no reason that any one of the fours numbers 1 4 should be more likely to occur for the second ball than the others. Still not convinced? Write out the all twelve ways that the two balls could be picked:

7 7 (1,2) (1,3) (1,4) (2,1) (2,3) (2,4) (3,1) (3,2) (3,4) (4,1) (4,2) (4,3) In 6 of these 12 cases, the second ball is odd. P(both odd) = P(first odd) P(second odd first odd) = = Review Question 9 A number is chosen at random from the first 10,000 positive integers. Find the probability that the number is: a perfect square (1, 4, 9, 16, 25, etc) divisible by 2 but not by 10 a three digit number ending in 7 or 9 divisible by 100 if you already know it is divisible by Question 9 Solution A number is chosen at random from the first 10,000 positive integers. P(perfect square) = ,000 = P(divisible by 2 but not by 10) = = 4 10 P(a three digit number ending in 7 or 9) = ,000 = P(divisible by 100 if you already know it is divisible by 250) = Review Question 10 Pick a number consisting of not more than six digits. What is the probability of a 9 being at least one of the digits?

8 8 22. Review Question 10 P(at least one 9) = 1 P(no digit is a 9) ( ) 6 9 = 1 =

### Let U = {Sun., Mon., Tue., Wed., Thur., Fri., Sat.} A = {Mon., Wed., Fri., Sat.}

MATH 102 Final Exam Practice Fall 2012 Use the information below to answer questions 1-4. Let U = {Sun., Mon., Tue., Wed., Thur., Fri., Sat.} A = {Mon., Wed., Fri., Sat.} B = {Sat., Sun.} C = {Tue., Wed.,

### Chapter 6. 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? Ans: 4/52.

Chapter 6 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? 4/52. 2. What is the probability that a randomly selected integer chosen from the first 100 positive

### Contemporary Mathematics- MAT 130. Probability. a) What is the probability of obtaining a number less than 4?

Contemporary Mathematics- MAT 30 Solve the following problems:. A fair die is tossed. What is the probability of obtaining a number less than 4? What is the probability of obtaining a number less than

### Chapter 15. Definitions: experiment: is the act of making an observation or taking a measurement.

MATH 11008: Probability Chapter 15 Definitions: experiment: is the act of making an observation or taking a measurement. outcome: one of the possible things that can occur as a result of an experiment.

### Hoover High School Math League. Counting and Probability

Hoover High School Math League Counting and Probability Problems. At a sandwich shop there are 2 kinds of bread, 5 kinds of cold cuts, 3 kinds of cheese, and 2 kinds of dressing. How many different sandwiches

### Example: If we roll a dice and flip a coin, how many outcomes are possible?

12.5 Tree Diagrams Sample space- Sample point- Counting principle- Example: If we roll a dice and flip a coin, how many outcomes are possible? TREE DIAGRAM EXAMPLE: Use a tree diagram to show all the possible

### STAB47S:2003 Midterm Name: Student Number: Tutorial Time: Tutor:

STAB47S:200 Midterm Name: Student Number: Tutorial Time: Tutor: Time: 2hours Aids: The exam is open book Students may use any notes, books and calculators in writing this exam Instructions: Show your reasoning

### MATH 105: Finite Mathematics 8-3: Expected Value

MATH 105: Finite Mathematics 8-3: Expected Value Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Introduction to Expected Value 2 Examples 3 Expected Value of a Bernoulli Process

### 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

### PROBABILITY. Chapter Overview Conditional Probability

PROBABILITY Chapter. Overview.. Conditional Probability If E and F are two events associated with the same sample space of a random experiment, then the conditional probability of the event E under the

### https://assessment.casa.uh.edu/assessment/printtest.htm PRINTABLE VERSION Quiz 10

1 of 8 4/9/2013 8:17 AM PRINTABLE VERSION Quiz 10 Question 1 Let A and B be events in a sample space S such that P(A) = 0.34, P(B) = 0.39 and P(A B) = 0.19. Find P(A B). a) 0.4872 b) 0.5588 c) 0.0256 d)

### What is the probability of throwing a fair die and receiving a six? Introduction to Probability. Basic Concepts

Basic Concepts Introduction to Probability A probability experiment is any experiment whose outcomes relies purely on chance (e.g. throwing a die). It has several possible outcomes, collectively called

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Ch. - Problems to look at 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

### number of equally likely " desired " outcomes numberof " successes " OR

Math 107 Probability and Experiments Events or Outcomes in a Sample Space: Probability: Notation: P(event occurring) = numberof waystheevent canoccur total number of equally likely outcomes number of equally

### 33 Probability: Some Basic Terms

33 Probability: Some Basic Terms In this and the coming sections we discuss the fundamental concepts of probability at a level at which no previous exposure to the topic is assumed. Probability has been

### The study of probability has increased in popularity over the years because of its wide range of practical applications.

6.7. Probability. The study of probability has increased in popularity over the years because of its wide range of practical applications. In probability, each repetition of an experiment is called a trial,

### I. WHAT IS PROBABILITY?

C HAPTER 3 PROBABILITY Random Experiments I. WHAT IS PROBABILITY? The weatherman on 0 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and

### 94 Counting Solutions for Chapter 3. Section 3.2

94 Counting 3.11 Solutions for Chapter 3 Section 3.2 1. Consider lists made from the letters T, H, E, O, R, Y, with repetition allowed. (a How many length-4 lists are there? Answer: 6 6 6 6 = 1296. (b

### Most of us would probably believe they are the same, it would not make a difference. But, in fact, they are different. Let s see how.

PROBABILITY If someone told you the odds of an event A occurring are 3 to 5 and the probability of another event B occurring was 3/5, which do you think is a better bet? Most of us would probably believe

### Math 141. Lecture 2: More Probability! Albyn Jones 1. jones@reed.edu www.people.reed.edu/ jones/courses/141. 1 Library 304. Albyn Jones Math 141

Math 141 Lecture 2: More Probability! Albyn Jones 1 1 Library 304 jones@reed.edu www.people.reed.edu/ jones/courses/141 Outline Law of total probability Bayes Theorem the Multiplication Rule, again Recall

### Math 1320 Chapter Seven Pack. Section 7.1 Sample Spaces and Events. Experiments, Outcomes, and Sample Spaces. Events. Complement of an Event

Math 1320 Chapter Seven Pack Section 7.1 Sample Spaces and Events Experiments, Outcomes, and Sample Spaces An experiment is an occurrence with a result, or outcome, that is uncertain before the experiment

### 4.4 Conditional Probability

4.4 Conditional Probability It is often necessary to know the probability of an event under restricted conditions. Recall the results of a survey of 100 Grade 12 mathematics students in a local high school.

### Lecture 11: Probability models

Lecture 11: Probability models Probability is the mathematical toolbox to describe phenomena or experiments where randomness occur. To have a probability model we need the following ingredients A sample

### Remember to leave your answers as unreduced fractions.

Probability Worksheet 2 NAME: Remember to leave your answers as unreduced fractions. We will work with the example of picking poker cards out of a deck. A poker deck contains four suits: diamonds, hearts,

### Lesson 1. Basics of Probability. Principles of Mathematics 12: Explained! www.math12.com 314

Lesson 1 Basics of Probability www.math12.com 314 Sample Spaces: Probability Lesson 1 Part I: Basic Elements of Probability Consider the following situation: A six sided die is rolled The sample space

### Definition and Calculus of Probability

In experiments with multivariate outcome variable, knowledge of the value of one variable may help predict another. For now, the word prediction will mean update the probabilities of events regarding the

### Week in Review #3 (L.1-L.2, )

Math 166 Week-in-Review - S. Nite 9/26/2012 Page 1 of 6 Week in Review #3 (L.1-L.2, 1.1-1.7) 1. onstruct a truth table for (p q) (p r) p Q R p q r p r ( p r) (p q) (p r) T T T T F F T T T T F T T T F F

### MATH 10: Elementary Statistics and Probability Chapter 3: Probability Topics

MATH 10: Elementary Statistics and Probability Chapter 3: Probability Topics Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides, you should

### Objectives To find probabilities of mutually exclusive and overlapping events To find probabilities of independent and dependent events

CC- Probability of Compound Events Common Core State Standards MACCS-CP Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model Also MACCS-CP MP, MP,

### Grade 7/8 Math Circles Fall 2012 Probability

1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Probability Probability is one of the most prominent uses of mathematics

### For two disjoint subsets A and B of Ω, say that A and B are disjoint events. For disjoint events A and B we take an axiom P(A B) = P(A) + P(B)

Basic probability A probability space or event space is a set Ω together with a probability measure P on it. This means that to each subset A Ω we associate the probability P(A) = probability of A with

### Section 6-5 Sample Spaces and Probability

492 6 SEQUENCES, SERIES, AND PROBABILITY 52. How many committees of 4 people are possible from a group of 9 people if (A) There are no restrictions? (B) Both Juan and Mary must be on the committee? (C)

### EXAM. Exam #3. Math 1430, Spring 2002. April 21, 2001 ANSWERS

EXAM Exam #3 Math 1430, Spring 2002 April 21, 2001 ANSWERS i 60 pts. Problem 1. A city has two newspapers, the Gazette and the Journal. In a survey of 1, 200 residents, 500 read the Journal, 700 read the

### Mathematics Teachers Enrichment Program MTEP 2012 Probability Solutions

Mathematics Teachers Enrichment Program MTEP 202 Probability Solutions. List the sample space for each of the following experiments: a) A card is drawn from a deck of playing cards and you are interested

### Section 6.2 Definition of Probability

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 that it will

### A magician showed a magic trick where he picked one card from a standard deck. Determine what the probability is that the card will be a queen card?

Topic : Probability Word Problems- Worksheet 1 Jill is playing cards with her friend when she draws a card from a pack of 20 cards numbered from 1 to 20. What is the probability of drawing a number that

### The numerator will be the number of bills that aren t fives (12) = 1 = = = 1 6

Section 4.2 Solutions: 1) In her wallet, Anne Kelly has 14 bills. Seven are \$1 bills, two are \$5 bills, four are \$10 bills and one is a \$20 bill. She passes a volunteer seeking donations for the Salvation

### Formula for Theoretical Probability

Notes Name: Date: Period: Probability I. Probability A. Vocabulary is the chance/ likelihood of some event occurring. Ex) The probability of rolling a for a six-faced die is 6. It is read as in 6 or out

### Normal Distribution Lecture Notes

Normal Distribution Lecture Notes Professor Richard Blecksmith richard@math.niu.edu Dept. of Mathematical Sciences Northern Illinois University Math 101 Website: http://math.niu.edu/ richard/math101 Section

### (b) You draw two balls from an urn and track the colors. When you start, it contains three blue balls and one red ball.

Examples for Chapter 3 Probability Math 1040-1 Section 3.1 1. Draw a tree diagram for each of the following situations. State the size of the sample space. (a) You flip a coin three times. (b) You draw

### Slide 1 Math 1520, Lecture 23. This lecture covers mean, median, mode, odds, and expected value.

Slide 1 Math 1520, Lecture 23 This lecture covers mean, median, mode, odds, and expected value. Slide 2 Mean, Median and Mode Mean, Median and mode are 3 concepts used to get a sense of the central tendencies

### Laws of probability. Information sheet. Mutually exclusive events

Laws of probability In this activity you will use the laws of probability to solve problems involving mutually exclusive and independent events. You will also use probability tree diagrams to help you

### The Binomial Probability Distribution

The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Objectives After this lesson we will be able to: determine whether a probability

### Elementary Statistics. Probability Rules with Venn & Tree Diagram

Probability Rules with Venn & Tree Diagram What are some basic Probability Rules? There are three basic Probability Rules: Complement Rule Addition Rule Multiplication Rule What is the Complement Rule?

### Homework 8 Solutions

CSE 21 - Winter 2014 Homework Homework 8 Solutions 1 Of 330 male and 270 female employees at the Flagstaff Mall, 210 of the men and 180 of the women are on flex-time (flexible working hours). Given that

### STAT 35A HW2 Solutions

STAT 35A HW2 Solutions http://www.stat.ucla.edu/~dinov/courses_students.dir/09/spring/stat35.dir 1. A computer consulting firm presently has bids out on three projects. Let A i = { awarded project i },

### CLAT Junction Maths Exercise

CLAT Junction Maths Exercise 16 www.clatjunction.com clatjunction@gmail.com 9472474746 Maths Exercise 16 1. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

### PROBABILITY. The theory of probabilities is simply the Science of logic quantitatively treated. C.S. PEIRCE

PROBABILITY 53 Chapter 3 PROBABILITY The theory of probabilities is simply the Science of logic quantitatively treated. C.S. PEIRCE 3. Introduction In earlier Classes, we have studied the probability as

### Probability (Day 1 and 2) Blue Problems. Independent Events

Probability (Day 1 and ) Blue Problems Independent Events 1. There are blue chips and yellow chips in a bag. One chip is drawn from the bag. The chip is placed back into the bag. A second chips is then

### MULTIPLE 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. Provide an appropriate response. 1) A coin is tossed. Find the probability that the result

### Odds: Odds compares the number of favorable outcomes to the number of unfavorable outcomes.

MATH 11008: Odds and Expected Value Odds: Odds compares the number of favorable outcomes to the number of unfavorable outcomes. Suppose all outcomes in a sample space are equally likely where a of them

### 35.4. Total Probability and Bayes Theorem. Introduction. Prerequisites. Learning Outcomes

Total Probability and Bayes Theorem 35.4 Introduction When the ideas of probability are applied to engineering (and many other areas) there are occasions when we need to calculate conditional probabilities

### Chapter 6. QTM1310/ Sharpe. Randomness and Probability. 6.1 Random Phenomena and Probability. 6.1 Random Phenomena and Probability

6.1 Random Phenomena and Probability Chapter 6 Randomness and Probability The Law of Large Numbers (LLN) states that if the events are independent, then as the number of trials increases, the longrun relative

### Math 421: Probability and Statistics I Note Set 2

Math 421: Probability and Statistics I Note Set 2 Marcus Pendergrass September 13, 2013 4 Discrete Probability Discrete probability is concerned with situations in which you can essentially list all the

### Math 240 Practice Exam 1 Note: Show all work whenever possible for full credit. You may leave your answers in terms of fractions.

Name: (Solution on last page)... Math 240 Practice Exam 1 Note: Show all work whenever possible for full credit. You may leave your answers in terms of fractions. Formulas: 2 2 x x n x x s x x n f x f

### 3. Examples of discrete probability spaces.. Here α ( j)

3. EXAMPLES OF DISCRETE PROBABILITY SPACES 13 3. Examples of discrete probability spaces Example 17. Toss n coins. We saw this before, but assumed that the coins are fair. Now we do not. The sample space

### PROBABILITY. SIMPLE PROBABILITY is the likelihood that a specific event will occur, represented by a number between 0 and 1.

PROBABILITY SIMPLE PROBABILITY SIMPLE PROBABILITY is the likelihood that a specific event will occur, represented by a number between 0 and. There are two categories of simple probabilities. THEORETICAL

### Conditional Probability

Conditional Probability We are given the following data about a basket of fruit: rotten not rotten total apple 3 6 9 orange 2 4 6 total 5 10 15 We can find the probability that a fruit is an apple, P (A)

### CHAPTER 3: PROBABILITY TOPICS

CHAPTER 3: PROBABILITY TOPICS Exercise 1. In a particular college class, there are male and female students. Some students have long hair and some students have short hair. Write the symbols for the probabilities

### Grade 7/8 Math Circles Fall 2012 Factors and Primes

1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Factors and Primes Factors Definition: A factor of a number is a whole

### Math 210 Lecture Notes: Chapter Matrix Product Inverse Matrix

Math 210 Lecture Notes: Chapter 2.5 2.6 Matrix Product Inverse Matrix Richard Blecksmith Dept. of Mathematical Sciences Northern Illinois University 1. Matrix Product A B Step 1. The Initial Matrices Step

### 7.1 Sample space, events, probability

7.1 Sample space, events, probability In this chapter, we will study the topic of probability which is used in many different areas including insurance, science, marketing, government and many other areas.

### P (A) = 0.60, P (B) = 0.55, P (A B c ) = 0.30

Probability Math 42 Test October, 20 Dr. Pendergrass On my honor, I have neither given nor received any aid on this work, nor am I aware of any breach of the Honor Code that I shall not immediately report.

### Game on. Suggested maths games for primary aged children. Useful tips on how to bring maths into the home.

Game on Suggested maths games for primary aged children Useful tips on how to bring maths into the home. Multiple wiggles 1. Count in ones from 0 to 50. 2. When you reach a multiple of 2, (2,4,6,8,10)

### Lecture 1 Introduction Properties of Probability Methods of Enumeration Asrat Temesgen Stockholm University

Lecture 1 Introduction Properties of Probability Methods of Enumeration Asrat Temesgen Stockholm University 1 Chapter 1 Probability 1.1 Basic Concepts In the study of statistics, we consider experiments

### Interlude: Practice Midterm 1

CONDITIONAL PROBABILITY AND INDEPENDENCE 38 Interlude: Practice Midterm 1 This practice exam covers the material from the first four chapters Give yourself 50 minutes to solve the four problems, which

### Fundamentals of Probability

Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible

### Probability OPRE 6301

Probability OPRE 6301 Random Experiment... Recall that our eventual goal in this course is to go from the random sample to the population. The theory that allows for this transition is the theory of probability.

### Edexcel Statistics 1 Probability. Section 2: Conditional Probability

Edexcel Statistics Probability Section 2: Conditional Probability Notes and Examples These notes contain sub-sections on: Getting information from a table Using tree diagrams Getting information from a

### Quadratic Equations and Inequalities

MA 134 Lecture Notes August 20, 2012 Introduction The purpose of this lecture is to... Introduction The purpose of this lecture is to... Learn about different types of equations Introduction The purpose

### Math 166:505 Fall 2013 Exam 2 - Version A

Name Math 166:505 Fall 2013 Exam 2 - Version A On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work. Signature: Instructions: Part I and II are multiple choice

### MATH 201. Final ANSWERS August 12, 2016

MATH 01 Final ANSWERS August 1, 016 Part A 1. 17 points) A bag contains three different types of dice: four 6-sided dice, five 8-sided dice, and six 0-sided dice. A die is drawn from the bag and then rolled.

### Assessment For The California Mathematics Standards Grade 6

Introduction: Summary of Goals GRADE SIX By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative

### Math 135A Homework Problems

Math 35A Homework Problems Homework Fifteen married couples are at a dance lesson Assume that male-female) dance pairs are assigned at random a) What is the number of possible assignments? b) What is the

### STAT 319 Probability and Statistics For Engineers PROBABILITY. Engineering College, Hail University, Saudi Arabia

STAT 319 robability and Statistics For Engineers LECTURE 03 ROAILITY Engineering College, Hail University, Saudi Arabia Overview robability is the study of random events. The probability, or chance, that

### 2. How many ways can the letters in PHOENIX be rearranged? 7! = 5,040 ways.

Math 142 September 27, 2011 1. How many ways can 9 people be arranged in order? 9! = 362,880 ways 2. How many ways can the letters in PHOENIX be rearranged? 7! = 5,040 ways. 3. The letters in MATH are

### Distributions. and Probability. Find the sample space of an experiment. Find the probability of an event. Sample Space of an Experiment

C Probability and Probability Distributions APPENDIX C.1 Probability A1 C.1 Probability Find the sample space of an experiment. Find the probability of an event. Sample Space of an Experiment When assigning

### Formula Sheet About Exam Study Tips Hub: Math Teacher Resources Index Old Exams Graphing Calculator Guidelines SED Links Math A Topic Headings

Regents Prep Math A Formula Sheet About Exam Study Tips Hub: Math Teacher Resources Index Old Exams Graphing Calculator Guidelines SED Links Math A Topic Headings Work is underway to create sites for the

### . Notice that this means P( A B )

Probability II onditional Probability You already know probabilities change when more information is known. For example the probability of getting type I diabetes for the general population is.06. The

### Review of Probability

Review of Probability Table of Contents Part I: Basic Equations and Notions Sample space Event Mutually exclusive Probability Conditional probability Independence Addition rule Multiplicative rule Using

### Lesson 48 Conditional Probability

(A) Opening Example #1: A survey of 500 adults asked about college expenses. The survey asked questions about whether or not the person had a child in college and about the cost of attending college. Results

### Math227 Homework (Probability Practices) Name

Math227 Homework (Probability Practices) Name 1) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the

### Massachusetts Institute of Technology

n (i) m m (ii) n m ( (iii) n n n n (iv) m m Massachusetts Institute of Technology 6.0/6.: Probabilistic Systems Analysis (Quiz Solutions Spring 009) Question Multiple Choice Questions: CLEARLY circle the

### Topic 6: Conditional Probability and Independence

Topic 6: September 15-20, 2011 One of the most important concepts in the theory of probability is based on the question: How do we modify the probability of an event in light of the fact that something

### Basic Probability. Probability: The part of Mathematics devoted to quantify uncertainty

AMS 5 PROBABILITY Basic Probability Probability: The part of Mathematics devoted to quantify uncertainty Frequency Theory Bayesian Theory Game: Playing Backgammon. The chance of getting (6,6) is 1/36.

### 1. Math richard/math101. M = monthly payment P = principal r = i/12 = monthly interest rate n = number of months

1. Math 101 Mortgages and Annuities Professor Richard Blecksmith richard@math.niu.edu Dept. of Mathematical Sciences Northern Illinois University http://math.niu.edu/ richard/math101 M = where 2. Monthly

### 2. Three dice are tossed. Find the probability of a) a sum of 4; or b) a sum greater than 4 (may use complement)

Probability Homework Section P4 1. A two-person committee is chosen at random from a group of four men and three women. Find the probability that the committee contains at least one man. 2. Three dice

### Combinatorial Proofs

Combinatorial Proofs Two Counting Principles Some proofs concerning finite sets involve counting the number of elements of the sets, so we will look at the basics of counting. Addition Principle: If A

### 6.3 Conditional Probability and Independence

222 CHAPTER 6. PROBABILITY 6.3 Conditional Probability and Independence Conditional Probability Two cubical dice each have a triangle painted on one side, a circle painted on two sides and a square painted

### AP Stats - Probability Review

AP Stats - Probability Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. I toss a penny and observe whether it lands heads up or tails up. Suppose

### Summer Math Reinforcement Packet Students Entering into 2 nd Grade

1 Summer Math Reinforcement Packet Students Entering into 2 nd Grade Our first graders had a busy year learning new math skills. Mastery of all these skills is extremely important in order to develop a

### Answer: = π cm. Solution:

Round #1, Problem A: (4 points/10 minutes) The perimeter of a semicircular region in centimeters is numerically equal to its area in square centimeters. What is the radius of the semicircle in centimeters?

### Name Date. Sample Spaces and Probability For use with Exploration 10.1

0. Sample Spaces and Probability For use with Exploration 0. Essential Question How can you list the possible outcomes in the sample space of an experiment? The sample space of an experiment is the set

### Factoring Polynomials

Factoring Polynomials Factoring Factoring is the process of writing a polynomial as the product of two or more polynomials. The factors of 6x 2 x 2 are 2x + 1 and 3x 2. In this section, we will be factoring

### MATH 105: Finite Mathematics 7-2: Properties of Probability

MATH 105: Finite Mathematics 7-2: Properties of Probability Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Probability of Combined Events 2 Probability and Venn Diagrams 3 Odds

### STATISTICS HIGHER SECONDARY - SECOND YEAR. Untouchability is a sin Untouchability is a crime Untouchability is inhuman

STATISTICS HIGHER SECONDARY - SECOND YEAR Untouchability is a sin Untouchability is a crime Untouchability is inhuman TAMILNADU TEXTBOOK CORPORATION College Road, Chennai- 600 006 i Government of Tamilnadu

### number of favorable outcomes total number of outcomes number of times event E occurred number of times the experiment was performed.

12 Probability 12.1 Basic Concepts Start with some Definitions: Experiment: Any observation of measurement of a random phenomenon is an experiment. Outcomes: Any result of an experiment is called an outcome.

### Probability and Counting

Probability and Counting Basic Counting Principles Permutations and Combinations Sample Spaces, Events, Probability Union, Intersection, Complements; Odds Conditional Probability, Independence Bayes Formula