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

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

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

Transcription

1 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 are tossed. Find the probability of a) a sum of 4; or b) a sum greater than 4 (may use complement) 3. A bag contains 6 red balls, 7 white balls, and 10 blue balls. A ball is chosen at random from the bag. Find the probability of choosing a ball that is not red. 4. One card is selected from a standard deck of 52 playing cards. What is the probability that the card is either a heart or a face card? 5. A jar contains seven white, six blue and ten red marbles. If one marble is drawn at random from the jar, find the probability that a) the marble is white or blue; b) the marble is white or red; c) the marble is blue or red. 6. A person removes two aces and a king from a deck of 52 playing cards and draws, without replacement, two more cards from the deck. In this game, order will matter because the person looks at each card as it is drawn. Drawing an ace of diamonds and then an ace of hearts is a different result than drawing an ace of hearts and then an ace of diamonds. Find the probability that the person will draw two aces or two kings or an ace and a king. 7. A coin and a die are tossed. Find the probability of getting a tail on the coin or a 3 on the die. 8. A survey claims that 70% of the households in a certain town have a color TV, 20 % have a microwave oven, and 2% have both a color TV and a microwave oven. Find the probability that a randomly selected household has either a color TV or a microwave oven. 9. The following table shows the probability that a customer at a department store will make a purchase in the indicated price range. Cost Probability Below $5.25 $5 - $ $20 - $ $40 - $ $70 - $ $100 - $ $150 or more.03 Find the probability that a customer makes a purchase that is a) less than $20 b) more than $99.99 c) $40 or more d) less than $100 1

2 10. The law firm of Able, Barron, Chalmers, Dowd, Erickson, and Franks has two senior partners: Able and Barron. Two of the attorneys are to be selected to attend a conference. Assuming all are equally likely to be selected find each probability. a) Chalmers is selected b) Able and Dowd are selected c) At least one senior partner is selected 11. A survey of 282,549 freshmen from the class of 2006 at 437 baccalaureate colleges and universities gave the following information: # of Colleges Applied to 1 2 or or more Percent(as decimal) Source: Higher Education Research Institute, UCLA, 2002 Find the probability of each event: a) The student applied to fewer than 4 colleges. b) The student applies to at least 2 colleges. c) The student applied to more than 3 colleges. d) The student applied to no colleges. 12. Forty-three percent of the world s population have type O blood, 85% of the world s population are Rh-positive, and 37% have type O blood and are Rh-positive. What is the probability that any individual will have type O blood or be Rh-positive? 13. According to the National Safety council, in 1994 there were 38,166 firearm deaths in the United States. Of these, 32,694 were males, were between the ages of 15 and 24, and 9809 were males between the ages of 15 and 24. a) What is the probability that a random person killed by firearms in 1994 was male or between the ages of 15 and 24? b) What is the probability that a random person killed by firearms in 1994 was neither male nor between the ages of 15 and 24? 14. Suppose 37% of those polled approve of the Republican candidate for president, 42% approve of the Democratic candidate for president, and 7% approve of both candidates. What is the probability that a randomly selected person approves of neither candidate? 15.According to the American Medical Association, in 1996 there were 737,764 physicians in the US. 157,387 were female, 133,005 were under the age of 35, and 47,348 of those under 35 were female. What is the probability that a randomly chosen physician in 1996 was female or under the age of 35? 16. Suppose that at a college, 53% of the students earn a degree at the end of four years, and 25% of the students earn a degree at the end of 5 years. What is the probability of earning a degree at the end of 4 or 5 years? 2

3 17. Suppose 18% of the students at a college have an academic scholarship that pays partial tuition, 43% of the students at the college have some need-based financial aid, and 52% of the students have need-based financial aid or an academic scholarship. What is the probability that a randomly selected student has both need-based financial aid and an academic scholarship? 18. Based on research conducted after the 1989 Loma Prieta earthquake, US Geological Survey (USGS) results indicate that there is a 62% probability of at least one quake of magnitude 6.7 or greater striking the San Francisco Bay region before a) If there is a 29% probability of two or more earthquakes of magnitude 6.7 or greater in that area before 2032, what is the probability of having exactly one earthquake of magnitude 6.7 or above in that area before 2032? b) What is the probability of no earthquake of 6.7 or above in the area before 2032? 3

4 Answers 1. (E would be a committee with no men) P(E ) =. So P(E) =1- = a) ; b) (use complement, E = sum less than or equal to 4) P(E) = E = not red; E = red; P(E ) =. P(E) = 1- P(E ) = The or means we want the union, so P(heart or face) = P(heart) + P(face) P(heart and face) =. 5. (Note that these are mutually exclusive, so there is no overlap) a ), b) c) (These are mutually exclusive) P(2 Aces) = = P(2 Kings) = P(Ace and king) =, So P(2 Aces or 2 kings or an ace and a king) =. 7. Note that the results are ordered pairs with a die result and a coin toss result in each order pair, such as (t,1) (t,2) etc. P(tail) + P(3) P (t 3) = = P(TV U Microware) = P (TV) + P(Micro) P(TV Micro) = = a) 0.62 b) 0.11 c) 0.27 d) a) Put Chalmers on and then choose one more n(e) = 1 C(5,1) = 5; n(s) = C(6,2) = 15; P(E) = 1/3 b) If you put both on you are done (there is only one way to do this) n(e) = 1; n(s) = 15; P(E) = 1/15 c) Either one partner or both are on. One senior partner: choose one of 2: C(2,1) and then choose second person C(4,1); so P(one senior partner) =. Put both on: P(both) = ; So P(at least one S.P) =. 11. a) 0.49 b) 0.8 c) 0.51 d) P(type O or Rh positive) = P(type O) + P(Rh positive) P( O & Rh positive) = = a) P(Male) + P( 15-24) P(Male and 15-24) = b) use complement: P(neither) =

5 P(approve of republican or democrat) = 1 ( ) = = 0.28 or 28%. 15. P(female) + P(under 35) P(female and under 35) = You cannot do both at the same time, so mutually exclusive. P(degree in 4 or 5 years) = 0.78 or 78%. 17. P (both) = P(scholarship) + P(need-based) P( scholarship or need-based) = = 0.09 or 9 %. 18. a) = 0.33 or 33% chance b) = 0.38 or 38% of no earthquake of 6.7 or above (of course there could be smaller earthquakes). 5

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

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.

More information

An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event

An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event is the sum of the probabilities of the outcomes in the

More information

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? 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

More information

33 Probability: Some Basic Terms

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

More information

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

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,

More information

Grade 7/8 Math Circles Fall 2012 Probability

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

More information

Chapter 5 - Probability

Chapter 5 - Probability Chapter 5 - Probability 5.1 Basic Ideas An experiment is a process that, when performed, results in exactly one of many observations. These observations are called the outcomes of the experiment. The set

More information

Section 6.2 Definition of Probability

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

More information

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

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

More information

PROBABILITY 14.3. section. The Probability of an Event

PROBABILITY 14.3. section. The Probability of an Event 4.3 Probability (4-3) 727 4.3 PROBABILITY In this section In the two preceding sections we were concerned with counting the number of different outcomes to an experiment. We now use those counting techniques

More information

A (random) experiment is an activity with observable results. The sample space S of an experiment is the set of all outcomes.

A (random) experiment is an activity with observable results. The sample space S of an experiment is the set of all outcomes. Chapter 7 Probability 7.1 Experiments, Sample Spaces, and Events A (random) experiment is an activity with observable results. The sample space S of an experiment is the set of all outcomes. Each outcome

More information

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

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

More information

Probability. Sample space: all the possible outcomes of a probability experiment, i.e., the population of outcomes

Probability. Sample space: all the possible outcomes of a probability experiment, i.e., the population of outcomes Probability Basic Concepts: Probability experiment: process that leads to welldefined results, called outcomes Outcome: result of a single trial of a probability experiment (a datum) Sample space: all

More information

Elementary Statistics. Probability Rules with Venn & Tree Diagram

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?

More information

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

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

More information

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

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)

More information

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

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

More information

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

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

More information

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

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

More information

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

(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

More information

4.4 Conditional Probability

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.

More information

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

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

More information

Homework 8 Solutions

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

More information

P (below P L or speak F L) = P (below P L) + P (speak F L) P (both) = = 0.311

P (below P L or speak F L) = P (below P L) + P (speak F L) P (both) = = 0.311 concordance=true 1. The American Community Survey is an ongoing survey that provides data every year to give communities the current information they need to plan investments and services. The 2010 American

More information

I. WHAT IS PROBABILITY?

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

More information

Math 3C Homework 3 Solutions

Math 3C Homework 3 Solutions Math 3C Homework 3 s Ilhwan Jo and Akemi Kashiwada ilhwanjo@math.ucla.edu, akashiwada@ucla.edu Assignment: Section 2.3 Problems 2, 7, 8, 9,, 3, 5, 8, 2, 22, 29, 3, 32 2. You draw three cards from a standard

More information

Sample Space, Events, and PROBABILITY

Sample Space, Events, and PROBABILITY Sample Space, Events, and 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.

More information

Hoover High School Math League. Counting and Probability

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

More information

Review of Probability

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

More information

Statistics 100A Homework 2 Solutions

Statistics 100A Homework 2 Solutions Statistics Homework Solutions Ryan Rosario Chapter 9. retail establishment accepts either the merican Express or the VIS credit card. total of percent of its customers carry an merican Express card, 6

More information

Basic Probability Theory II

Basic Probability Theory II RECAP Basic Probability heory II Dr. om Ilvento FREC 408 We said the approach to establishing probabilities for events is to Define the experiment List the sample points Assign probabilities to the sample

More information

Chapter 4 - Practice Problems 2

Chapter 4 - Practice Problems 2 Chapter - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. 1) If you flip a coin three times, the

More information

Probability --QUESTIONS-- Principles of Math 12 - Probability Practice Exam 1 www.math12.com

Probability --QUESTIONS-- Principles of Math 12 - Probability Practice Exam 1 www.math12.com 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 information

+ Section 6.2 and 6.3

+ Section 6.2 and 6.3 Section 6.2 and 6.3 Learning Objectives After this section, you should be able to DEFINE and APPLY basic rules of probability CONSTRUCT Venn diagrams and DETERMINE probabilities DETERMINE probabilities

More information

Definition and Calculus of Probability

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

More information

Math 150 Sample Exam #2

Math 150 Sample Exam #2 Problem 1. (16 points) TRUE or FALSE. a. 3 die are rolled, there are 1 possible outcomes. b. If two events are complementary, then they are mutually exclusive events. c. If A and B are two independent

More information

Section Tree Diagrams. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section Tree Diagrams. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 12.5 Tree Diagrams What You Will Learn Counting Principle Tree Diagrams 12.5-2 Counting Principle If a first experiment can be performed in M distinct ways and a second experiment can be performed

More information

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

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.

More information

Consider a system that consists of a finite number of equivalent states. The chance that a given state will occur is given by the equation.

Consider a system that consists of a finite number of equivalent states. The chance that a given state will occur is given by the equation. Probability and the Chi-Square Test written by J. D. Hendrix Learning Objectives Upon completing the exercise, each student should be able: to determine the chance that a given state will occur in a system

More information

7.1 Sample space, events, probability

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.

More information

Basic Probability Theory I

Basic Probability Theory I A Probability puzzler!! Basic Probability Theory I Dr. Tom Ilvento FREC 408 Our Strategy with Probability Generally, we want to get to an inference from a sample to a population. In this case the population

More information

Chapter 14 From Randomness to Probability

Chapter 14 From Randomness to Probability Chapter 14 From Randomness to Probability 199 Chapter 14 From Randomness to Probability 1. Sample spaces. a) S = { HH, HT, TH, TT} All of the outcomes are equally likely to occur. b) S = { 0, 1, 2, 3}

More information

Find the indicated probability. 1) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.

Find the indicated probability. 1) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. Math 0 Practice Test 3 Fall 2009 Covers 7.5, 8.-8.3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. ) If a single

More information

2.5 Conditional Probabilities and 2-Way Tables

2.5 Conditional Probabilities and 2-Way Tables 2.5 Conditional Probabilities and 2-Way Tables Learning Objectives Understand how to calculate conditional probabilities Understand how to calculate probabilities using a contingency or 2-way table It

More information

Math/Stats 425 Introduction to Probability. 1. Uncertainty and the axioms of probability

Math/Stats 425 Introduction to Probability. 1. Uncertainty and the axioms of probability Math/Stats 425 Introduction to Probability 1. Uncertainty and the axioms of probability Processes in the real world are random if outcomes cannot be predicted with certainty. Example: coin tossing, stock

More information

Lesson 1: Experimental and Theoretical Probability

Lesson 1: Experimental and Theoretical Probability Lesson 1: Experimental and Theoretical Probability Probability is the study of randomness. For instance, weather is random. In probability, the goal is to determine the chances of certain events happening.

More information

CHAPTER 3: PROBABILITY TOPICS

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

More information

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0.

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0. Name: Date:. For each of the following scenarios, determine the appropriate distribution for the random variable X. A) A fair die is rolled seven times. Let X = the number of times we see an even number.

More information

AP Stats - Probability Review

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

More information

Laws of probability. Information sheet. Mutually exclusive events

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

More information

Conditional Probability and General Multiplication Rule

Conditional Probability and General Multiplication Rule Conditional Probability and General Multiplication Rule Objectives: - Identify Independent and dependent events - Find Probability of independent events - Find Probability of dependent events - Find Conditional

More information

Section 6-5 Sample Spaces and Probability

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)

More information

Chapter 5 Section 2 day 1 2014f.notebook. November 17, 2014. Honors Statistics

Chapter 5 Section 2 day 1 2014f.notebook. November 17, 2014. Honors Statistics Chapter 5 Section 2 day 1 2014f.notebook November 17, 2014 Honors Statistics Monday November 17, 2014 1 1. Welcome to class Daily Agenda 2. Please find folder and take your seat. 3. Review Homework C5#3

More information

4.3. Addition and Multiplication Laws of Probability. Introduction. Prerequisites. Learning Outcomes. Learning Style

4.3. Addition and Multiplication Laws of Probability. Introduction. Prerequisites. Learning Outcomes. Learning Style Addition and Multiplication Laws of Probability 4.3 Introduction When we require the probability of two events occurring simultaneously or the probability of one or the other or both of two events occurring

More information

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

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.

More information

4.5 Finding Probability Using Tree Diagrams and Outcome Tables

4.5 Finding Probability Using Tree Diagrams and Outcome Tables 4.5 Finding Probability Using ree Diagrams and Outcome ables Games of chance often involve combinations of random events. hese might involve drawing one or more cards from a deck, rolling two dice, or

More information

Chapter 14 From Randomness to Probability

Chapter 14 From Randomness to Probability 226 Part IV Randomness and Probability Chapter 14 From Randomness to Probability 1. Roulette. If a roulette wheel is to be considered truly random, then each outcome is equally likely to occur, and knowing

More information

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

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

More information

Lesson 48 Conditional Probability

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

More information

Chapter 4 - Practice Problems 1

Chapter 4 - Practice Problems 1 Chapter 4 - Practice Problems SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. ) Compare the relative frequency formula

More information

MAT 1000. Mathematics in Today's World

MAT 1000. Mathematics in Today's World MAT 1000 Mathematics in Today's World We talked about Cryptography Last Time We will talk about probability. Today There are four rules that govern probabilities. One good way to analyze simple probabilities

More information

I. WHAT IS PROBABILITY?

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

More information

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

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

More information

Chapter 4: Probabilities and Proportions

Chapter 4: Probabilities and Proportions Stats 11 (Fall 2004) Lecture Note Introduction to Statistical Methods for Business and Economics Instructor: Hongquan Xu Chapter 4: Probabilities and Proportions Section 4.1 Introduction In the real world,

More information

The Addition Rule and Complements Page 1. Blood Types. The purpose of this activity is to introduce you to the addition rules of probability.

The Addition Rule and Complements Page 1. Blood Types. The purpose of this activity is to introduce you to the addition rules of probability. The Addition Rule and Complements Page 1 Blood Types The purpose of this activity is to introduce you to the addition rules of probability. The addition rules of probability are used to find the probabilities

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Practice Test Chapter 9 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the odds. ) Two dice are rolled. What are the odds against a sum

More information

Toss a coin twice. Let Y denote the number of heads.

Toss a coin twice. Let Y denote the number of heads. ! Let S be a discrete sample space with the set of elementary events denoted by E = {e i, i = 1, 2, 3 }. A random variable is a function Y(e i ) that assigns a real value to each elementary event, e i.

More information

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.

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

More information

Jan 17 Homework Solutions Math 151, Winter 2012. Chapter 2 Problems (pages 50-54)

Jan 17 Homework Solutions Math 151, Winter 2012. Chapter 2 Problems (pages 50-54) Jan 17 Homework Solutions Math 11, Winter 01 Chapter Problems (pages 0- Problem In an experiment, a die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample

More information

Probability. A random sample is selected in such a way that every different sample of size n has an equal chance of selection.

Probability. A random sample is selected in such a way that every different sample of size n has an equal chance of selection. 1 3.1 Sample Spaces and Tree Diagrams Probability This section introduces terminology and some techniques which will eventually lead us to the basic concept of the probability of an event. The Rare Event

More information

Topic : Probability of a Complement of an Event- Worksheet 1. Do the following:

Topic : Probability of a Complement of an Event- Worksheet 1. Do the following: Topic : Probability of a Complement of an Event- Worksheet 1 1. You roll a die. What is the probability that 2 will not appear 2. Two 6-sided dice are rolled. What is the 3. Ray and Shan are playing football.

More information

A Simple Example. Sample Space and Event. Tree Diagram. Tree Diagram. Probability. Probability - 1. Probability and Counting Rules

A Simple Example. Sample Space and Event. Tree Diagram. Tree Diagram. Probability. Probability - 1. Probability and Counting Rules Probability and Counting Rules researcher claims that 10% of a large population have disease H. random sample of 100 people is taken from this population and examined. If 20 people in this random sample

More information

Probability. a number between 0 and 1 that indicates how likely it is that a specific event or set of events will occur.

Probability. a number between 0 and 1 that indicates how likely it is that a specific event or set of events will occur. Probability Probability Simple experiment Sample space Sample point, or elementary event Event, or event class Mutually exclusive outcomes Independent events a number between 0 and 1 that indicates how

More information

. Notice that this means P( A B )

. 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

More information

Probability Review. ICPSR Applied Bayesian Modeling

Probability Review. ICPSR Applied Bayesian Modeling Probability Review ICPSR Applied Bayesian Modeling Random Variables Flip a coin. Will it be heads or tails? The outcome of a single event is random, or unpredictable What if we flip a coin 10 times? How

More information

PROBABILITY NOTIONS. Summary. 1. Random experiment

PROBABILITY NOTIONS. Summary. 1. Random experiment PROBABILITY NOTIONS Summary 1. Random experiment... 1 2. Sample space... 2 3. Event... 2 4. Probability calculation... 3 4.1. Fundamental sample space... 3 4.2. Calculation of probability... 3 4.3. Non

More information

Basic concepts in probability. Sue Gordon

Basic concepts in probability. Sue Gordon Mathematics Learning Centre Basic concepts in probability Sue Gordon c 2005 University of Sydney Mathematics Learning Centre, University of Sydney 1 1 Set Notation You may omit this section if you are

More information

INTRODUCTION TO PROBABILITY AND STATISTICS

INTRODUCTION TO PROBABILITY AND STATISTICS INTRODUCTION TO PROBABILITY AND STATISTICS Conditional probability and independent events.. A fair die is tossed twice. Find the probability of getting a 4, 5, or 6 on the first toss and a,,, or 4 on the

More information

CHAPTER 4: DISCRETE RANDOM VARIABLE

CHAPTER 4: DISCRETE RANDOM VARIABLE CHAPTER 4: DISCRETE RANDOM VARIABLE Exercise 1. A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following

More information

Probability and Venn diagrams UNCORRECTED PAGE PROOFS

Probability and Venn diagrams UNCORRECTED PAGE PROOFS Probability and Venn diagrams 12 This chapter deals with further ideas in chance. At the end of this chapter you should be able to: identify complementary events and use the sum of probabilities to solve

More information

1 Combinations, Permutations, and Elementary Probability

1 Combinations, Permutations, and Elementary Probability 1 Combinations, Permutations, and Elementary Probability Roughly speaking, Permutations are ways of grouping things where the order is important. Combinations are ways of grouping things where the order

More information

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

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

More information

Worked examples Basic Concepts of Probability Theory

Worked examples Basic Concepts of Probability Theory Worked examples Basic Concepts of Probability Theory Example 1 A regular tetrahedron is a body that has four faces and, if is tossed, the probability that it lands on any face is 1/4. Suppose that one

More information

**Chance behavior is in the short run but has a regular and predictable pattern in the long run. This is the basis for the idea of probability.

**Chance behavior is in the short run but has a regular and predictable pattern in the long run. This is the basis for the idea of probability. AP Statistics Chapter 5 Notes 5.1 Randomness, Probability,and Simulation In tennis, a coin toss is used to decide which player will serve first. Many other sports use this method because it seems like

More information

Stats Review Chapters 5-6

Stats Review Chapters 5-6 Stats Review Chapters 5-6 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

More information

For 2 coins, it is 2 possible outcomes for the first coin AND 2 possible outcomes for the second coin

For 2 coins, it is 2 possible outcomes for the first coin AND 2 possible outcomes for the second coin Problem Set 1. 1. If you have 10 coins, how many possible combinations of heads and tails are there for all 10 coins? Hint: how many combinations for one coin; two coins; three coins? Here there are 2

More information

34 Probability and Counting Techniques

34 Probability and Counting Techniques 34 Probability and Counting Techniques If you recall that the classical probability of an event E S is given by P (E) = n(e) n(s) where n(e) and n(s) denote the number of elements of E and S respectively.

More information

Massachusetts Institute of Technology

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

More information

Probabilistic Strategies: Solutions

Probabilistic Strategies: Solutions Probability Victor Xu Probabilistic Strategies: Solutions Western PA ARML Practice April 3, 2016 1 Problems 1. You roll two 6-sided dice. What s the probability of rolling at least one 6? There is a 1

More information

Exam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR.

Exam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR. Exam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR. 1. Urn A contains 6 white marbles and 4 red marbles. Urn B contains 3 red marbles and two white

More information

Chapter 4 Probability

Chapter 4 Probability The Big Picture of Statistics Chapter 4 Probability Section 4-2: Fundamentals Section 4-3: Addition Rule Sections 4-4, 4-5: Multiplication Rule Section 4-7: Counting (next time) 2 What is probability?

More information

Remember to leave your answers as unreduced fractions.

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,

More information

Math 118 Study Guide. This study guide is for practice only. The actual question on the final exam may be different.

Math 118 Study Guide. This study guide is for practice only. The actual question on the final exam may be different. Math 118 Study Guide This study guide is for practice only. The actual question on the final exam may be different. Convert the symbolic compound statement into words. 1) p represents the statement "It's

More information

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

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. Find the mean for the given sample data. 1) Bill kept track of the number of hours he spent

More information

Probability of Compound Events

Probability of Compound Events Probability of Compound Events Why? Then You calculated simple probability. (Lesson 0-11) Now Find probabilities of independent and dependent events. Find probabilities of mutually exclusive events. Online

More information

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

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

More information

If we know that LeBron s next field goal attempt will be made in a game after 3 days or more rest, it would be natural to use the statistic

If we know that LeBron s next field goal attempt will be made in a game after 3 days or more rest, it would be natural to use the statistic Section 7.4: Conditional Probability and Tree Diagrams Sometimes our computation of the probability of an event is changed by the knowledge that a related event has occurred (or is guaranteed to occur)

More information

Exam. Name. How many distinguishable permutations of letters are possible in the word? 1) CRITICS

Exam. Name. How many distinguishable permutations of letters are possible in the word? 1) CRITICS Exam Name How many distinguishable permutations of letters are possible in the word? 1) CRITICS 2) GIGGLE An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm,

More information

MTH 110 Chapter 6 Practice Test Problems

MTH 110 Chapter 6 Practice Test Problems MTH 0 Chapter 6 Practice Test Problems Name ) Probability A) assigns realistic numbers to random events. is the branch of mathematics that studies long-term patterns of random events by repeated observations.

More information

AP Statistics 7!3! 6!

AP Statistics 7!3! 6! Lesson 6-4 Introduction to Binomial Distributions Factorials 3!= Definition: n! = n( n 1)( n 2)...(3)(2)(1), n 0 Note: 0! = 1 (by definition) Ex. #1 Evaluate: a) 5! b) 3!(4!) c) 7!3! 6! d) 22! 21! 20!

More information