# Homework 20: Compound Probability

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Homework 20: Compound Probability Definition The probability of an event is defined to be the ratio of times that you expect the event to occur after many trials: number of equally likely outcomes resulting in event A P( A) number of equally likely outcomes possible Properties 1. Imagine rolling two dice, one red and one green, many times. a. How often do you expect to get a 4 on the red die? b. Of the times you get a 4 on the red die, how often do you expect to get a 3 on the green die? c. What proportion of rolls would you expect to get a 4 on the red die and a 3 on the green die? d. What proportion of rolls would you expect to get either a 1 or a 2 on the red die? e. What proportion of rolls would you expect to get either a 4 on the red die or a 3 on the green die?

2 2. A regular deck of cards has 52 cards 13 of each suit (clubs, diamonds, hearts, and spades) and 4 of each number (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A). a. Find the probability of drawing an A from a complete deck. b. Suppose you just drew an A from a complete deck, and now draw a second card. Find the probability that the second card is at 10, J, Q, or K. c. Find the probability of drawing an A and then a 10/J/Q/K. d. Find the probability of drawing two cards and getting blackjack (an A and 10/J/Q/K, in either order). e. Find the probability of drawing two cards and not getting blackjack. 3. Suppose you pull one card from a complete deck of cards. a. What is the probability of getting either a 7 or a heart? b. What is the probability of drawing a card that is not a 7 or a heart? c. Draw a Venn diagram that is related to these problems.

3 4. Suppose you draw two cards from a deck. a. What is the probability that both cards are hearts? b. Find the complement of the previous probability. Describe this event in simple, everyday language. 5. Suppose you draw five cards from a deck. What is the probability that they are all the same suit? 6. Six spot Keno is a casino game with the following possible prizes (based on a \$1 bet): Prize \$1 \$4 \$88 \$1500 -\$1 (lose) Probability 12.98% 2.85% 0.31% 0.01% a. Compute the probability of losing. b. Freddy is going to play 6-spot Keno twice. What is the probability that he loses both times? c. What is the probability that Freddy wins at least one prize, if he plays twice? That is, what is the probability that he does not lose both times? d. Suppose Freddy decides to play 10 times what is the probability that he loses all 10 games? e. What is the probability that Freddy wins at least one prize, if he plays 10 times?

4 7. Richie is betting on a horse race. There are 8 horses in the race, with equal chances of winning. Richie bet that horses A, B, and C will finish in the top three, in any order. a. What is the probability that horse A comes in first, B comes in second, and C comes in third? b. What is the probability that any of Richie s three horses finishes first? c. What is the probability that one of Richie s horses finishes first and another of Richie s horses finishes second? d. What is the probability that Richie s three horses finish in the top 3 spots? 8. After going on an Easter egg hunt, Amy s basket has the following contents: 2 chocolate bunnies 5 chocolate eggs 1 real hard-boiled eggs 4 marshmallow bunnies Her little brother sticks his hand into the basket and pulls out the first thing he touches. a. What is the probability that he selects a bunny or an egg? b. What is the probability that he selects something chocolate? c. What is the probability that he selects some kind of egg? d. What is the probability that he selects a chocolate egg? e. What is the probability that he selects an egg or something chocolate? f. What is the probability that he does not get an egg or something chocolate? g. Draw a Venn diagram that relates to the previous set of problems. h. Suppose Amy s brother manages to reach into the basket twice and gets two treats. What is the probability that both things are chocolate? i. What is the probability that Amy s brother gets two treats, and neither one is chocolate? That is, the first one is not chocolate, and the second one is not chocolate. j. What is the probability that Amy s brother gets at least one chocolate?

5 9. There are six people in the school math club. Information is given about each of them: Angela Buster Chris Deidre Edwina Fiona 6 th 6 th 6 th 7 th 7 th 8 th Girl Boy Boy Girl Girl Girl The club needs to choose a president. They have decided to do this by drawing a name from a hat. a. What is the probability that a 7 th grader will be chosen as president? b. What is the probability that the president is not a 7 th grader? c. What is the probability that a 6 th grader will be chosen as president? d. What is the probability that a 6 th grader or a 7 th grader will be chosen as president? e. What is the probability that a girl will be chosen as president? f. What is the probability that the president is either a girl or a 6 th grader? g. Draw a Venn diagram showing the probabilities relevant to the previous problem. 10. The math club from the previous set of problems also needs to choose a vice-president. After drawing the president s name from the hat, they will draw a second name to be vicepresident. a. On the back of this page, make a tree showing all of the possible president/vicepresident combinations. (You may use the students initials, instead of writing their entire names.) b. How many possible ways are there to fill the two offices? Show how you can answer this using multiplication. c. How many possible outcomes have girls as both president and vice-president? Show how you can answer this question using multiplication. d. What is the probability that girls are chosen for both the president and the vicepresident?

### 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

### The Casino Lab STATION 1: CRAPS

The Casino Lab Casinos rely on the laws of probability and expected values of random variables to guarantee them profits on a daily basis. Some individuals will walk away very wealthy, while others will

### 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.

### 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

### 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

### 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..

### 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

### Chapter 3: Probability

Chapter 3: Probability We see probabilities almost every day in our real lives. Most times you pick up the newspaper or read the news on the internet, you encounter probability. There is a 65% chance of

### 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

### PROBABILITY. Thabisa Tikolo STATISTICS SOUTH AFRICA

PROBABILITY Thabisa Tikolo STATISTICS SOUTH AFRICA Probability is a topic that some educators tend to struggle with and thus avoid teaching it to learners. This is an indication that teachers are not yet

### Math 210. 1. Compute C(1000,2) (a) 499500. (b) 1000000. (c) 2. (d) 999000. (e) None of the above.

Math 210 1. Compute C(1000,2) (a) 499500. (b) 1000000. (c) 2. (d) 999000. 2. Suppose that 80% of students taking calculus have previously had a trigonometry course. Of those that did, 75% pass their calculus

### PROBABILITY C A S I N O L A B

A P S T A T S A Fabulous PROBABILITY C A S I N O L A B AP Statistics Casino Lab 1 AP STATISTICS CASINO LAB: INSTRUCTIONS The purpose of this lab is to allow you to explore the rules of probability in the

### 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.

### Introduction to Discrete Probability. Terminology. Probability definition. 22c:19, section 6.x Hantao Zhang

Introduction to Discrete Probability 22c:19, section 6.x Hantao Zhang 1 Terminology Experiment A repeatable procedure that yields one of a given set of outcomes Rolling a die, for example Sample space

### 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

### 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

### 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

### 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

### Question of the Day. Key Concepts. Vocabulary. Mathematical Ideas. QuestionofDay

QuestionofDay Question of the Day What is the probability that in a family with two children, both are boys? What is the probability that in a family with two children, both are boys, if we already know

### 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

### Conducting Probability Experiments

CHAPTE Conducting Probability Experiments oal Compare probabilities in two experiments. ame. Place a shuffled deck of cards face down.. Turn over the top card.. If the card is an ace, you get points. A

### Lesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations)

Lesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations) Note: At my school, there is only room for one math main lesson block in ninth grade. Therefore,

### 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.

### Standard 12: The student will explain and evaluate the financial impact and consequences of gambling.

TEACHER GUIDE 12.1 GAMBLING PAGE 1 Standard 12: The student will explain and evaluate the financial impact and consequences of gambling. Risky Business Priority Academic Student Skills Personal Financial

### Probability and Random Variables (Rees: )

Probability and Random Variables (Rees:. -.) Earlier in this course, we looked at methods of describing the data in a sample. Next we would like to have models for the ways in which data can arise. Before

### 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

### Grade Level Year Total Points Core Points % At Standard %

Performance Assessment Task Marble Game task aligns in part to CCSSM HS Statistics & Probability Task Description The task challenges a student to demonstrate an understanding of theoretical and empirical

### **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

### 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

### Lab 11. Simulations. The Concept

Lab 11 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

### 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

### 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

### 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

### Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific

Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific Name: The point value of each problem is in the left-hand margin. You

### 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

### 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

### (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

### Introduction and Overview

Introduction and Overview Probability and Statistics is a topic that is quickly growing, has become a major part of our educational program, and has a substantial role in the NCTM Standards. While covering

### 21 Easter Activities For Kids

21 Easter Activities For Kids Happy Easter From Copyright 2011 Teresa Evans. All rights reserved. You are free to give this book to others. You may not alter the book in any way. You may not claim copyright.

### 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

### 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

### Standard 12: The student will explain and evaluate the financial impact and consequences of gambling.

STUDENT MODULE 12.1 GAMBLING PAGE 1 Standard 12: The student will explain and evaluate the financial impact and consequences of gambling. Risky Business Simone, Paula, and Randy meet in the library every

### 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

### High School Statistics and Probability Common Core Sample Test Version 2

High School Statistics and Probability Common Core Sample Test Version 2 Our High School Statistics and Probability sample test covers the twenty most common questions that we see targeted for this level.

### 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

### All You Ever Wanted to Know About Probability Theory, but Were Afraid to Ask

All You Ever Wanted to Know About Probability Theory, but Were Afraid to Ask 1 Theoretical Exercises 1. Let p be a uniform probability on a sample space S. If S has n elements, what is the probability

### Chapter 4: Probability and Counting Rules

Chapter 4: Probability and Counting Rules Learning Objectives Upon successful completion of Chapter 4, you will be able to: Determine sample spaces and find the probability of an event using classical

### LESSON PLAN. Unit: Probability Lesson 6 Date: Summer 2008

LESSON PLAN Grade Level/Course: Grade 6 Mathematics Teacher(s): Ms. Green & Mr. Nielsen Unit: Probability Lesson 6 Date: Summer 2008 Topic(s): Playing Carnival Games Resources: Transparencies: Worksheets:

### 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 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,

### MATH 105: Finite Mathematics 6-5: Combinations

MATH 105: Finite Mathematics 6-5: Combinations Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Developing Combinations 2 s of Combinations 3 Combinations vs. Permutations 4 Conclusion

### Decision Making Under Uncertainty. Professor Peter Cramton Economics 300

Decision Making Under Uncertainty Professor Peter Cramton Economics 300 Uncertainty Consumers and firms are usually uncertain about the payoffs from their choices Example 1: A farmer chooses to cultivate

### Probability: The Study of Randomness Randomness and Probability Models. IPS Chapters 4 Sections 4.1 4.2

Probability: The Study of Randomness Randomness and Probability Models IPS Chapters 4 Sections 4.1 4.2 Chapter 4 Overview Key Concepts Random Experiment/Process Sample Space Events Probability Models Probability

### 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,

### Determine the empirical probability that a person selected at random from the 1000 surveyed uses Mastercard.

Math 120 Practice Exam II Name You must show work for credit. 1) A pair of fair dice is rolled 50 times and the sum of the dots on the faces is noted. Outcome 2 4 5 6 7 8 9 10 11 12 Frequency 6 8 8 1 5

### Possibilities and Probabilities

Possibilities and Probabilities Counting The Basic Principle of Counting: Suppose that two experiments are to be performed. Then if experiment 1 can result in any one of m possible outcomes and if, for

### 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

### 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

### 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

### Responsible Gambling Education Unit: Mathematics A & B

The Queensland Responsible Gambling Strategy Responsible Gambling Education Unit: Mathematics A & B Outline of the Unit This document is a guide for teachers to the Responsible Gambling Education Unit:

### Combinatorics 3 poker hands and Some general probability

Combinatorics 3 poker hands and Some general probability Play cards 13 ranks Heart 4 Suits Spade Diamond Club Total: 4X13=52 cards You pick one card from a shuffled deck. What is the probability that it

### Lesson 6. Identifying Prisms. Daksha and his brother and sister are playing a dice game. When a die is rolled, one number is displayed on the top.

Math 4 Lesson 6 Identifying Prisms Dice Games Daksha and his brother and sister are playing a dice game. When a die is rolled, one number is displayed on the top. When you roll the dice they will only

### 36 Odds, Expected Value, and Conditional Probability

36 Odds, Expected Value, and Conditional Probability What s the difference between probabilities and odds? To answer this question, let s consider a game that involves rolling a die. If one gets the face

### Elementary Statistics and Inference. Elementary Statistics and Inference. 16 The Law of Averages (cont.) 22S:025 or 7P:025.

Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 20 1 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter 16 (cont.) 2 D. Making a Box Model Key Questions regarding box What numbers

### 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.

### 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

### If a tennis player was selected at random from the group, find the probability that the player is

Basic Probability. The table below shows the number of left and right handed tennis players in a sample of 0 males and females. Left handed Right handed Total Male 3 29 32 Female 2 6 8 Total 4 0 If a tennis

### 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.

### Christopher Maue Sarah Crowley

Christopher Maue Sarah Crowley maue9678@fredonia.edu crow3853@fredonia.edu What are the Chances? Introduction: This lesson involves unique probability mini-projects for teachers to use with their students.

### Pure Math 30: Explained! 334

www.puremath30.com 334 Lesson 2, Part One: Basic Combinations Basic combinations: In the previous lesson, when using the fundamental counting principal or permutations, the order of items to be arranged

### 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

### 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

### 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

### Counting principle, permutations, combinations, probabilities

Counting Methods Counting principle, permutations, combinations, probabilities Part 1: The Fundamental Counting Principle The Fundamental Counting Principle is the idea that if we have a ways of doing

### SPANISH 21. 3. Player blackjack always beats a dealer blackjack and is paid 3 to 2.

SPANISH 21 Spanish 21 is standard blackjack with optional bonus wagers. All rules pertaining to blackjack as posted on the WSGC website will remain the same and are not altered in this game except as noted

### Cinch Card Game - The Rules and how to play

Cinch Card Game - The Rules and how to play This document provides you with the rules and then an explanation how to play with some examples. Have fun! The Rules Terms to understand: Trick: one card from

### Week 5: Expected value and Betting systems

Week 5: Expected value and Betting systems Random variable A random variable represents a measurement in a random experiment. We usually denote random variable with capital letter X, Y,. If S is the sample

### 2urbo Blackjack 21.99. 2 9 Hold their face value

2urbo Blackjack Type of Game The game of 2urbo Blackjack utilizes a player-dealer position and is a California game. The player-dealer shall collect all losing wagers, pay all winning wagers, and may not

### to name the four suits of cards to sort the pack into suits the names ace, king, queen, jack the value of the cards- ie ace is highest, 2 is lowest.

1 Lesson 1 Today we are learning: to name the four suits of cards to sort the pack into suits the names ace, king, queen, jack the value of the cards- ie ace is highest, 2 is lowest. one pack of cards

### 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

### 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)

### In the situations that we will encounter, we may generally calculate the probability of an event

What does it mean for something to be random? An event is called random if the process which produces the outcome is sufficiently complicated that we are unable to predict the precise result and are instead

### Grade 6 Math Circles Mar.21st, 2012 Probability of Games

University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 6 Math Circles Mar.21st, 2012 Probability of Games Gambling is the wagering of money or something of

### Lesson 5: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities Bellringer

Lesson 5: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities Bellringer Use the following information below to answer the two following questions: Students are playing a game

### A-Level Maths. in a week. Core Maths - Co-ordinate Geometry of Circles. Generating and manipulating graph equations of circles.

A-Level Maths in a week Core Maths - Co-ordinate Geometry of Circles Generating and manipulating graph equations of circles. Statistics - Binomial Distribution Developing a key tool for calculating probability

### 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

### LET S MAKE A DEAL! ACTIVITY

LET S MAKE A DEAL! ACTIVITY NAME: DATE: SCENARIO: Suppose you are on the game show Let s Make A Deal where Monty Hall (the host) gives you a choice of three doors. Behind one door is a valuable prize.

### Random Variables. 9. Variation 1. Find the standard deviations of the random variables in Exercise 1.

Random Variables 1. Expected value. Find the expected value of each random variable: a) x 10 20 30 P(X=x) 0.3 0.5 0.2 b) x 2 4 6 8 P(X=x) 0.3 0.4 0.2 0.1 2. Expected value. Find the expected value of each

### Section 7C: The Law of Large Numbers

Section 7C: The Law of Large Numbers Example. You flip a coin 00 times. Suppose the coin is fair. How many times would you expect to get heads? tails? One would expect a fair coin to come up heads half

### 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

### Elementary Statistics and Inference. Elementary Statistics and Inference. 17 Expected Value and Standard Error. 22S:025 or 7P:025.

Elementary Statistics and Inference S:05 or 7P:05 Lecture Elementary Statistics and Inference S:05 or 7P:05 Chapter 7 A. The Expected Value In a chance process (probability experiment) the outcomes of

### Mathematical goals. Starting points. Materials required. Time needed

Level S2 of challenge: B/C S2 Mathematical goals Starting points Materials required Time needed Evaluating probability statements To help learners to: discuss and clarify some common misconceptions about

### 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.

### PERMUTATIONS AND COMBINATIONS

PERMUTATIONS AND COMBINATIONS Mathematics for Elementary Teachers: A Conceptual Approach New Material for the Eighth Edition Albert B. Bennett, Jr., Laurie J. Burton and L. Ted Nelson Math 212 Extra Credit

### Ch. 13.3: More about Probability

Ch. 13.3: More about Probability Complementary Probabilities Given any event, E, of some sample space, U, of a random experiment, we can always talk about the complement, E, of that event: this is the

### 5.1.1 The Idea of Probability

5.1.1 The Idea of Probability Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. This remarkable fact is the basis for the idea of probability.

### Name Date. Goal: Understand and represent the intersection and union of two sets.

F Math 12 3.3 Intersection and Union of Two Sets p. 162 Name Date Goal: Understand and represent the intersection and union of two sets. A. intersection: The set of elements that are common to two or more