Save this PDF as:

Size: px
Start display at page:

## Transcription

2 Addition Rule for non-mutually exclusive events: 2a. I will select one card from the deck. What is the probability that I will select a face card? 2b. I will select one card from the deck. What is the probability that I will select a red card? 2c. I will select one card from the deck. What is the probability that I will select a face card that is red (event red and face card )? I will select one card from the deck. The two events Red and face card are not mutually exclusive, meaning they could happen at the same time. What is the probability that I will get a red card or a face card? You can do this problem two different ways. The two methods are outlined below. 2d. The number of total possibilities is 52. Count the number of successes in a deck, that is the number of cards that are face cards or red. Form the probability by dividing the two. 2e. The formula for the probability of two non-mutually exclusive events A or B occurring is as follows. P(A or B) = P(A) + P(B) P(A and B) Use this formula and the answers in parts a through c to compute the desired probability. Notice it matches the answer gotten in part d. (Show work.)

3 Multiplication Rule for Independent events: 3a. I will select two cards from a deck by selecting one, replacing it in the deck, and then selecting another. What is the probability that the first card is red? 3b. I will select two cards from a deck by selecting one, replacing it in the deck, and then selecting another. What is the probability that the second card is a Queen? 3c. I will select two cards from a deck by selecting one, replacing it in the deck, and then selecting another. What is the probability that I select a red card and then a Queen? Notice the two events first red and second Queen are independent since the occurrence of one does not affect the other (because we are replacing the first card before selecting the second). The formula for the probability of independent events A and B occurring is as follows. P(A and B) = P(A) * P(B) Use this formula and the answers to parts a and b to answer the question What is the probability that I select a red card and then a Queen?

4 Multiplication Rule for non-independent events: 4a. I will select a card from the deck, and without replacing it, select another. What is the probability the first card is red? 4b. I will select a card from the deck, and without replacing it, select another. Assuming the first card is red, what is the probability the second card is red? (Think about the total number of possibilities and the number of successes left in the deck.) This probability will be denoted by P( second red given first red ). 4c. I will select a card from the deck, and without replacing it, select another. What is the probability both cards are red? The formula for the probability of two nonindependent events A and B occurring is as follows. P(A and B) = P(A) * P(B given A) Use this formula and the answers to parts a and b to answer the question What is the probability both cards are red?

5 More practice: For the following problems, think about the events involved. Are they independent or mutually exclusive? What are the individual probabilities? What formula will you use? 5. I roll a six-sided die and toss a coin. What is the probability I get a Heads and a 6? 6. I roll three dice. What is the probability that I get three ones? 7. I draw a card from a poker deck, replace it, and draw another. What is the probability I get two Aces? 8. I draw a card from a poker deck, and without replacing it, draw another. What is the probability I get two Aces? 9. I roll a white six-sided die and a red six-sided die. What is the probability that I get a 1 on either die? (To be a success here, either the white die is 1, the red die is 1, or both dice are 1.) 10. I roll a six-sided die. What is the probability that I get a 5 or 6?

### 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

### 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

### 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,

### 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

### 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

### 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

### Probability. Experiment - any happening for which the result is uncertain. Outcome the possible result of the experiment

Probability Definitions: Experiment - any happening for which the result is uncertain Outcome the possible result of the experiment Sample space the set of all possible outcomes of the experiment 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

### 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.

### 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

### 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

### 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

### 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.

### 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.

### 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

### 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

### 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

### 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

### 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

### 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

### (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

### 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

### 7.5 Conditional Probability; Independent Events

7.5 Conditional Probability; Independent Events Conditional Probability Example 1. Suppose there are two boxes, A and B containing some red and blue stones. The following table gives the number of stones

### Combinations If 5 sprinters compete in a race, how many different ways can the medals for first, second and third place, be awarded

Combinations If 5 sprinters compete in a race, how many different ways can the medals for first, second and third place, be awarded If 5 sprinters compete in a race and the fastest 3 qualify for the relay

### 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

### 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

### 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

### 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.

### Poker. 10,Jack,Queen,King,Ace. 10, Jack, Queen, King, Ace of the same suit Five consecutive ranks of the same suit that is not a 5,6,7,8,9

Poker Poker is an ideal setting to study probabilities. Computing the probabilities of different will require a variety of approaches. We will not concern ourselves with betting strategies, however. Our

### 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

### Math 141. Lecture 1: Conditional Probability. Albyn Jones 1. 1 Library jones/courses/141

Math 141 Lecture 1: Conditional Probability Albyn Jones 1 1 Library 304 jones@reed.edu www.people.reed.edu/ jones/courses/141 Last Time Definitions: Sample Space, Events Last Time Definitions: Sample Space,

### Chapter 15. Probability, continued. The sample space of a random experiment is the set of all possible outcomes of the experiment.

Chapter 15. Probability, continued Review: The sample space of a random experiment is the set of all possible outcomes of the experiment. We have to count outcomes; a useful tool is the multiplication

### Probability Worksheet

Probability Worksheet 1. A single die is rolled. Find the probability of rolling a 2 or an odd number. 2. Suppose that 37.4% of all college football teams had winning records in 1998, and another 24.8%

### 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

### 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

### 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

### LECTURE 3. Probability Computations

LECTURE 3 Probability Computations Pg. 67, #42 is one of the hardest problems in the course. The answer is a simple fraction there should be a simple way to do it. I don t know a simple way I used the

### BRIEF SOLUTIONS. Basic Probability WEEK THREE. This worksheet relates to chapter four of the text book (Statistics for Managers 4 th Edition).

BRIEF SOLUTIONS Basic Probability WEEK THREE This worksheet relates to chapter four of the text book (Statistics for Managers 4 th Edition). This topic is the one many students find the most difficult.

### Statistics 1040 Summer 2009 Exam III NAME. Point score Curved Score

Statistics 1040 Summer 2009 Exam III NAME Point score Curved Score Each question is worth 10 points. There are 12 questions, so a total of 120 points is possible. No credit will be given unless your answer

### Unit 1: Probability. Experimental Probability: - probability that came from a simulation such as tossing dice, coins etc.

pplied Math 0 Unit : Probability Unit : Probability.: Experimental and Theoretical Probability Experimental Probability: - probability that came from a simulation such as tossing dice, coins etc. inomial

### In this chapter, we use sample data to make conclusions about the population. Many of these conclusions are based on probabilities of the events.

Lecture#4 Chapter 4: Probability In this chapter, we use sample data to make conclusions about the population. Many of these conclusions are based on probabilities of the events. 4-2 Fundamentals Definitions:

### 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

### 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

### 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

### Probability definitions

Probability definitions 1. Probability of an event = chance that the event will occur. 2. Experiment = any action or process that generates observations. In some contexts, we speak of a data-generating

### Statistical Inference. Prof. Kate Calder. If the coin is fair (chance of heads = chance of tails) then

Probability Statistical Inference Question: How often would this method give the correct answer if I used it many times? Answer: Use laws of probability. 1 Example: Tossing a coin If the coin is fair (chance

### Topic : Tree Diagrams- 5-Pack A - Worksheet Choose between 2 brands of jeans: Levi s and Allen Cooper.

Topic : Tree Diagrams- 5-Pack A - Worksheet 1 1. Three colors of balls that are In red, green and blue color are rolled simultaneously. a black color blazer of medium size among brown and black blazer

### Curriculum Design for Mathematic Lesson Probability

Curriculum Design for Mathematic Lesson Probability This curriculum design is for the 8th grade students who are going to learn Probability and trying to show the easiest way for them to go into this class.

### 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

### 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

### 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

### 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

### AQA Statistics 1. Probability. Section 2: Tree diagrams

Notes and Examples AQA Statistics Probability Section 2: Tree diagrams These notes include sub-sections on; Reminder of the addition and multiplication rules Probability tree diagrams Problems involving

### Probability. Section 9. Probability. Probability of A = Number of outcomes for which A happens Total number of outcomes (sample space)

Probability Section 9 Probability Probability of A = Number of outcomes for which A happens Total number of outcomes (sample space) In this section we summarise the key issues in the basic probability

### 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

### 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

### STAT 201 INTRODUCTION TO BUSINESS STATISTICS PROBABILITY REVIEW QUESTIONS

STAT 201 INTRODUCTION TO BUSINESS STATISTICS PROBABILITY REVIEW QUESTIONS Question 1: Five standard six-sided dice are rolled. What is the probability of getting the same number on all five dice? The probability

### 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)

### 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.

### 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

### 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

### Chapter 3: The basic concepts of probability

Chapter 3: The basic concepts of probability Experiment: a measurement process that produces quantifiable results (e.g. throwing two dice, dealing cards, at poker, measuring heights of people, recording

### 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

### 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

### MIDTERM EXAMINATION Spring 2009 STA301- Statistics and Probability (Session - 2)

MIDTERM EXAMINATION Spring 2009 STA301- Statistics and Probability (Session - 2) Question No: 1 Median can be found only when: Data is Discrete Data is Attributed Data is continuous Data is continuous

### 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

### Exam. Name. Find the number of subsets of the set. 1) {x x is an even number between 11 and 31} 2) {-13, 0, 13, 14, 15}

Exam Name Find the number of subsets of the set. 1) {x x is an even number between 11 and 31} 2) {-13, 0, 13, 1, 15} Let A = 6,, 1, 3, 0, 8, 9. Determine whether the statement is true or false. 3) 9 A

### 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

### 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

### 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

### POKER LOTTO LOTTERY GAME CONDITIONS These Game Conditions apply, until amended or revised, to the POKER LOTTO lottery game.

POKER LOTTO LOTTERY GAME CONDITIONS These Game Conditions apply, until amended or revised, to the POKER LOTTO lottery game. 1.0 Rules 1.1 POKER LOTTO is governed by the Rules Respecting Lottery Games of

### 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.

### 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.

### 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

### 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

### PROBABILITY. Chapter Overview

Chapter 6 PROBABILITY 6. Overview Probability is defined as a quantitative measure of uncertainty a numerical value that conveys the strength of our belief in the occurrence of an event. The probability

### Bayesian Tutorial (Sheet Updated 20 March)

Bayesian Tutorial (Sheet Updated 20 March) Practice Questions (for discussing in Class) Week starting 21 March 2016 1. What is the probability that the total of two dice will be greater than 8, given 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

### + 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

### MATHEMATICS 154, SPRING 2010 PROBABILITY THEORY Outline #3 (Combinatorics, bridge, poker)

Last modified: February, 00 References: MATHEMATICS 5, SPRING 00 PROBABILITY THEORY Outline # (Combinatorics, bridge, poker) PRP(Probability and Random Processes, by Grimmett and Stirzaker), Section.7.

### 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

### 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

### 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

### 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

### 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..

### 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

### 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,

### 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

### 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

### STAT 270 Probability Basics

STAT 270 Probability Basics Richard Lockhart Simon Fraser University Spring 2015 Surrey 1/28 Purposes of These Notes Jargon: experiment, sample space, outcome, event. Set theory ideas and notation: intersection,

### 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.

### 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)

### Probability And Odds Examples

Probability And Odds Examples. Will the Cubs or the Giants be more likely to win the game? What is the chance of drawing an ace from a deck of cards? What are the possibilities of rain today? What are

### PROBABILITY II BEGINNER CIRCLE 4/21/2013

PROBABILITY II BEGINNER CIRCLE 4/21/2013 1. WARM-UP: GOING SHOPPING The math circle instructors go to the store to shop. The set of all items in the store will be called S, and there is a function that

### 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

### 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

### 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