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

Size: px
Start display at page:

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

Transcription

1 Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results: Outcome Frequency (a) What is the experimental probability of rolling a 5? P (5) (b) What is the theoretical probability of rolling a 5? P (5) (c) What is the experimental probability of rolling a multiple of 3? P (multiple of 3) (d) What is the theoretical probability of rolling a multiple of 3? P (multiple of 3)

2 Math 102 Page 2 2. One card is drawn from a standard 52 card deck. What is the probability of drawing: (a) the queen of hearts? P (queen of hearts) 1 52 (b) a queen? P (queen) (c) a heart? P (heart) (d) a face card (J, Q, or K)? P (face card) Two -sided dice are rolled. What is the probability of rolling (a) a total of? There are 5 ways to get a total of {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)} so we have P (total of ) 5 3 (b) not a total of? This is simply the complement of the event in part (a), so we have P (not a total of ) 1 P (total of )

3 Math 102 Page 3 (c) total of or 7? The keyword or means we are looking for the probability of a union, namely P (total of total of 7). To find this we need P (total of ), P (total of 7), and P (total of total of 7). We computed P (total of ) in part (a). There are ways to get a total of 7 {(1, ), (2, 5), (3, 4), (4, 3), (5, 2), (, 1)} so we have P (total of 7) 3 1 Also note that P (total of total of 7) 0 since it is impossible to have a total of and a total of 7 simultaneously. Thus we have P (total of total of 7) P (total of ) + P ( total of 7) P (total of total of 7) (d) total of or more? The probability of getting a total of or more is the complement of the probability of getting a total of 2, 3, 4, or 5. There is only one way to get a total of 2, 2 ways to get a total of 3, 3 ways to get a total of 4 and 4 ways to get a total of 5. Also, the four events (getting a total of 2, a total of 3, a total of 4 and total of 5) are mutually exclusive. Thus we have P (total of or more) 1 P (total of 2, 3, 4, or 5) ( 1 P (total of 2) + P (total of 3) ) +P (total of 4) + P (total of 5) ( )

4 Math 102 Page 4 4. A gumball machine has gumballs of five flavors. There are 10 apple, 15 berry, 12 cherry, 8 orange, and 9 mint. When a quarter is put into the machine, it dispenses 5 gumballs at random. What is the probability that (a) each gumball is a different flavor? There are gumballs in the machine and 3, 12, 510 ways to choose any 5 of the gumballs. There are 54C 5 54! 39!5! 10C 1 15 C 1 12 C 1 8 C 1 9 C , 00 ways to choose one of each flavor. So the probability of selecting one gumball of each flavor is P (one of each flavor) 10 C 1 15 C 1 12 C 1 8 C 1 9 C 1 129, 00 3, 12, , C 5 (b) at least two gumballs are the same flavor? This is the complement of the event in part (a), so we have P (at least 2 same flavor) 1 P (one of each) , , , A coin is tossed ten times in a row. Find the probability that (a) no tails show. The probability that no tails show is the same as the probability that all heads show. This is the probability that the first coin is heads AND the second coin is heads AND... so we have an intersection of independent events.

6 Math 102 Page the 3 groups which is 3!. So we have 15C 5 10 C 5 5 C 5 3! 15! 10!5! 10! 5! 5!5! 5!1! 3! ! , 75 12, Five cards are drawn from a standard 52 card deck. What is the probability of drawing (a) 5 cards of the same color? P (5 of same color) , 998 (b) a full house (3 cards of one rank and two cards of a different rank)? The number of ways to draw any 5 cards is 52 C 5 2, 598, 90. The number of ways to get a full house is # ways to # of ways to # of ways to # of ways to pick rank for pick suits for pick rank pick suits 3 of a kind 3 of a kind for pair for pair 13C 1 4C 3 12C 1 4C 2 which is So the probability of drawing a full house is P (full house)

7 Math 102 Page 7 8. Suppose a jar has 4 coins: a penny, a nickel, a dime and a quarter. You remove two coins at random without replacement. Let A be the event you remove the quarter. Let B be the event you remove the dime. Let C be the event you remove less than 12 cents. (a) List the sample space. S {(p, n), (p, d), (p, q), (n, p), (n, d), (n, q), (d, p), (d, n), (d, q), (q, p), (q, n), (q, d)} (b) Draw a probability tree diagram to represent the possible scenarios. (c) Which pair(s) of theses events is (are) mutually exclusive? A {(p, q), (n, q), (d, q), (q, p), (q, n), (q, d)} B {(p, d), (n, d), (d, p), (d, n), (d, q), (q, d)} C {(p, n), (p, d), (n, p), (d, p)} So A B {(d, q), (q, d)} A C B C {(p, d), (d, p)} Thus only A and C are mutually exclusive.

8 Math 102 Page 8 (d) Find P (A), P (C), and P (B). P (A) P (C) P (B) (e) Compute and interpret P (A B) and P (B C). P (A B) is the probability that either A or B occurs, that is the probability that either a quarter or dime is removed. P (A B) P (A) + P (B) P (A B) P (B C) is the probability that either B or C occurs, that is the probability that either a dime or less than 12 cents is removed. P (B C) P (B) + P (C) P (B C) A dental assistant randomly sampled 200 patients and classified them according to whether or not they had a least one cavity in their last checkup and according to what type of tooth decay preventative measures they used. The information is as follows

9 Math 102 Page 9 At least one cavity No Cavities Brush only 9 2 Brush and floss only Brush and tooth sealants only Brush, floss and tooth sealants 3 4 If a patient is picked at random from this group, find the probability that (a) the patient had a least one cavity. The number of patients with at least one cavity is and the total number of patients is 200 so P (at least one cavity) (b) the patient brushes only. The number of patients that brush only is and the total number of patients is 200 so P (only brush) (c) the patient had no cavities, given s/he brushes, flosses and has tooth sealants. The number of patients that have no cavities and brush, floss and use sealants is 4. So the probability a patient has no cavities and brushes, flosses and uses sealants is P (no cavities brush, floss, and sealant) The number of patients that brush, floss and use sealants is so the probability a patient brushes, flosses and uses sealants is P (brush, floss, and sealants)

10 Math 102 Page 10 Thus the probability that a patient has no cavities, given s/he brushes, flosses and uses sealants is P (no cavities brush, floss, and sealants) P (no cavities brush, floss, and sealants) P (brush, floss, and sealants) (d) the patient brushes only, given that s/he had at least one cavity. The number of patients that only brush and have at least one cavity is 9. So the probability a patient only brushes and has at least one cavity is P (only brushes at least one cavity) The number of patients that have at least one cavity is so the probability a patient has at least one cavity is P (at least one cavity) Thus the probability that a patient brushes only, given s/he has at least one cavity is P (brushes only at least one cavity) P (brushes only at least one cavity) P (at least one cavity) A small college has two calculus classes. The first class has 25 students, 15 of whom are female, and the other class has 18 students, 8 of whom are female. One of the classes is selected at random and then two students are randomly selected from the class for an interview. If both of the students are female, what is the probability they came from the first class?

11 Math 102 Page 11 Call the first class Class A and the second class Class B. Then we have the following data So we get the following probability tree Female Male Class A Class B 8 10 From the tree we see that the probability of choosing class A and choosing two females is P (A 2 females) The probability of choosing two females is P (2 females) Thus the probability of choosing class A, given that two females were chosen is P (A 2 females) P (A 2 females) P (2 females) The probability is 0. that a student will study for an exam. If the student studies, she has a 0.8 chance of getting an A on the exam. If she does not study, she has a 0.3 probability of getting an A. Make a probability tree for this situation. What is the probability that she gets an A? If she gets an A, what is the conditional probability that

12 Math 102 Page 12 she studied? We get the following probability tree (where S denotes study, N denotes not study, A denotes gets an A and NA denotes does not get an A) From the tree we see that P (A) We also know that P (S A) so we have P (S A) P (S A) P (A)

13 Math 102 Page If you consider the value of a roll of a single -sided die to be the number that is rolled, what is the expected value of the roll of a single die? E ( ) 1 (1) + ( ) 1 (2) + ( ) 1 (3) + ( ) 1 (4) + ( ) 1 (5) + ( ) 1 () Consider a game that consists of drawing a single card at random from a standard 52 card deck. You pay \$3 to play the game and the \$3 is not returned. If you draw an ace you win \$10. If you draw a king or a queen, you win \$5. How much should you expect to win or lose on average if you play this game? E ( ) ( ) 4 8 (10 3) + (5 3) ( ) ( ) ( (7) + (2) ) ( 3) ( ) 40 (0 3) 52 You would expect to loose \$1.4.

14 Math 102 Page Suppose you just inherited \$100, 000 and you are trying to decide how to invest it for the next year. You have narrowed it down to two choices. The first choice is to invest it in a bond with a guaranteed return of 5% interest at the end of the year. The second choice is to bet it all on the Super Bowl with a 51% chance of doubling your money and a 49% chance of losing it all. Which investment option has the highest expected value? The bond has an expected value of E (1)(100, , ) 105, 000 Betting on the Super Bowl has an expected value of E (0.51)(200, 000) + (0.49)(0) 102, 000 So the bond has the higher expected value.

### 4.1 Sample Spaces and Events

4.1 Sample Spaces and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment is called an

### 7.1 Experiments, Sample Spaces, and Events

7.1 Experiments, Sample Spaces, and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment

### PROBABILITY. 1. Introduction. Candidates should able to:

PROBABILITY Candidates should able to: evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g for the total score when two fair dice are thrown), or by calculation

### Probability Rules. 2) The probability, P, of any event ranges from which of the following?

Name: WORKSHEET : Date: Answer the following questions. 1) Probability of event E occurring is... P(E) = Number of ways to get E/Total number of outcomes possible in S, the sample space....if. 2) The probability,

### Unit 19 Probability Review

. What is sample space? All possible outcomes Unit 9 Probability Review 9. I can use the Fundamental Counting Principle to count the number of ways an event can happen. 2. What is the difference between

### Probability Test Review Math 2. a. What is? b. What is? c. ( ) d. ( )

Probability Test Review Math 2 Name 1. Use the following venn diagram to answer the question: Event A: Odd Numbers Event B: Numbers greater than 10 a. What is? b. What is? c. ( ) d. ( ) 2. In Jason's homeroom

### The Teachers Circle Mar. 20, 2012 HOW TO GAMBLE IF YOU MUST (I ll bet you \$5 that if you give me \$10, I ll give you \$20.)

The Teachers Circle Mar. 2, 22 HOW TO GAMBLE IF YOU MUST (I ll bet you \$ that if you give me \$, I ll give you \$2.) Instructor: Paul Zeitz (zeitzp@usfca.edu) Basic Laws and Definitions of Probability If

### 4.3 Rules of Probability

4.3 Rules of Probability If a probability distribution is not uniform, to find the probability of a given event, add up the probabilities of all the individual outcomes that make up the event. Example:

### Probability. Ms. Weinstein Probability & Statistics

Probability Ms. Weinstein Probability & Statistics Definitions Sample Space The sample space, S, of a random phenomenon is the set of all possible outcomes. Event An event is a set of outcomes of a random

### TEST A CHAPTER 11, PROBABILITY

TEST A CHAPTER 11, PROBABILITY 1. Two fair dice are rolled. Find the probability that the sum turning up is 9, given that the first die turns up an even number. 2. Two fair dice are rolled. Find the probability

### Def: The intersection of A and B is the set of all elements common to both set A and set B

Def: Sample Space the set of all possible outcomes Def: Element an item in the set Ex: The number "3" is an element of the "rolling a die" sample space Main concept write in Interactive Notebook Intersection:

### Intermediate Math Circles November 1, 2017 Probability I

Intermediate Math Circles November 1, 2017 Probability I Probability is the study of uncertain events or outcomes. Games of chance that involve rolling dice or dealing cards are one obvious area of application.

### Exam III Review Problems

c Kathryn Bollinger and Benjamin Aurispa, November 10, 2011 1 Exam III Review Problems Fall 2011 Note: Not every topic is covered in this review. Please also take a look at the previous Week-in-Reviews

### Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include your name and student ID.

Math 3201 Unit 3 Probability Test 1 Unit Test Name: Part 1 Selected Response: Instructions: Choose the best answer and shade in the corresponding letter on the answer sheet provided. Be sure to include

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

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

### 10-8 Probability of Compound Events

Use any method to find the total number of outcomes in each situation. 6. Nathan has 4 t-shirts, 4 pairs of shorts, and 2 pairs of flip-flops. Use the Fundamental Counting Principle to find the number

### Math 1313 Section 6.2 Definition of Probability

Math 1313 Section 6.2 Definition of Probability Probability is a measure of the likelihood that an event occurs. For example, if there is a 20% chance of rain tomorrow, that means that the probability

### Chapter 11: Probability and Counting Techniques

Chapter 11: Probability and Counting Techniques Diana Pell Section 11.3: Basic Concepts of Probability Definition 1. A sample space is a set of all possible outcomes of an experiment. Exercise 1. An experiment

### Probability MAT230. Fall Discrete Mathematics. MAT230 (Discrete Math) Probability Fall / 37

Probability MAT230 Discrete Mathematics Fall 2018 MAT230 (Discrete Math) Probability Fall 2018 1 / 37 Outline 1 Discrete Probability 2 Sum and Product Rules for Probability 3 Expected Value MAT230 (Discrete

### Chapter 3: PROBABILITY

Chapter 3 Math 3201 1 3.1 Exploring Probability: P(event) = Chapter 3: PROBABILITY number of outcomes favourable to the event total number of outcomes in the sample space An event is any collection of

### Grade 6 Math Circles Fall Oct 14/15 Probability

1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2014 - Oct 14/15 Probability Probability is the likelihood of an event occurring.

### Chapter 1. Probability

Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.

### Answer each of the following problems. Make sure to show your work.

Answer each of the following problems. Make sure to show your work. 1. A board game requires each player to roll a die. The player with the highest number wins. If a player wants to calculate his or her

### SECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability

SECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability Name Period Write all probabilities as fractions in reduced form! Use the given information to complete problems 1-3. Five students have the

### Name: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11

Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value

### Raise your hand if you rode a bus within the past month. Record the number of raised hands.

166 CHAPTER 3 PROBABILITY TOPICS Raise your hand if you rode a bus within the past month. Record the number of raised hands. Raise your hand if you answered "yes" to BOTH of the first two questions. Record

### Empirical (or statistical) probability) is based on. The empirical probability of an event E is the frequency of event E.

Probability and Statistics Chapter 3 Notes Section 3-1 I. Probability Experiments. A. When weather forecasters say There is a 90% chance of rain tomorrow, or a doctor says There is a 35% chance of a successful

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

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

### 8.2 Union, Intersection, and Complement of Events; Odds

8.2 Union, Intersection, and Complement of Events; Odds Since we defined an event as a subset of a sample space it is natural to consider set operations like union, intersection or complement in the context

### Chapter 13 Test Review

1. The tree diagrams below show the sample space of choosing a cushion cover or a bedspread in silk or in cotton in red, orange, or green. Write the number of possible outcomes. A 6 B 10 C 12 D 4 Find

### 3 The multiplication rule/miscellaneous counting problems

Practice for Exam 1 1 Axioms of probability, disjoint and independent events 1. Suppose P (A) = 0.4, P (B) = 0.5. (a) If A and B are independent, what is P (A B)? What is P (A B)? (b) If A and B are disjoint,

### Math Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.

Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166 - Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 7.1 - Experiments, Sample Spaces,

### Math Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.

Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166 - Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 7.1 - Experiments, Sample Spaces,

### Key Concepts. Theoretical Probability. Terminology. Lesson 11-1

Key Concepts Theoretical Probability Lesson - Objective Teach students the terminology used in probability theory, and how to make calculations pertaining to experiments where all outcomes are equally

### Probability and Counting Techniques

Probability and Counting Techniques Diana Pell (Multiplication Principle) Suppose that a task consists of t choices performed consecutively. Suppose that choice 1 can be performed in m 1 ways; for each

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

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

### Probability. Probabilty Impossibe Unlikely Equally Likely Likely Certain

PROBABILITY Probability The likelihood or chance of an event occurring If an event is IMPOSSIBLE its probability is ZERO If an event is CERTAIN its probability is ONE So all probabilities lie between 0

### Unit 11 Probability. Round 1 Round 2 Round 3 Round 4

Study Notes 11.1 Intro to Probability Unit 11 Probability Many events can t be predicted with total certainty. The best thing we can do is say how likely they are to happen, using the idea of probability.

### 3 The multiplication rule/miscellaneous counting problems

Practice for Exam 1 1 Axioms of probability, disjoint and independent events 1 Suppose P (A 0, P (B 05 (a If A and B are independent, what is P (A B? What is P (A B? (b If A and B are disjoint, what is

### Such a description is the basis for a probability model. Here is the basic vocabulary we use.

5.2.1 Probability Models When we toss a coin, we can t know the outcome in advance. What do we know? We are willing to say that the outcome will be either heads or tails. We believe that each of these

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

Study Guide for Test III (MATH 1630) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the number of subsets of the set. 1) {x x is an even

### Probability and Randomness. Day 1

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

### Most of the time we deal with theoretical probability. Experimental probability uses actual data that has been collected.

AFM Unit 7 Day 3 Notes Theoretical vs. Experimental Probability Name Date Definitions: Experiment: process that gives a definite result Outcomes: results Sample space: set of all possible outcomes Event:

### CS1802 Week 9: Probability, Expectation, Entropy

CS02 Discrete Structures Recitation Fall 207 October 30 - November 3, 207 CS02 Week 9: Probability, Expectation, Entropy Simple Probabilities i. What is the probability that if a die is rolled five times,

### Part 1: I can express probability as a fraction, decimal, and percent

Name: Pattern: Part 1: I can express probability as a fraction, decimal, and percent For #1 to #4, state the probability of each outcome. Write each answer as a) a fraction b) a decimal c) a percent Example:

### Chapter 1: Sets and Probability

Chapter 1: Sets and Probability Section 1.3-1.5 Recap: Sample Spaces and Events An is an activity that has observable results. An is the result of an experiment. Example 1 Examples of experiments: Flipping

### Mutually Exclusive Events Algebra 1

Name: Mutually Exclusive Events Algebra 1 Date: Mutually exclusive events are two events which have no outcomes in common. The probability that these two events would occur at the same time is zero. Exercise

### Chapter 1. Probability

Chapter 1. Probability 1.1 Basic Concepts Scientific method a. For a given problem, we define measures that explains the problem well. b. Data is collected with observation and the measures are calculated.

### INDEPENDENT AND DEPENDENT EVENTS UNIT 6: PROBABILITY DAY 2

INDEPENDENT AND DEPENDENT EVENTS UNIT 6: PROBABILITY DAY 2 WARM UP Students in a mathematics class pick a card from a standard deck of 52 cards, record the suit, and return the card to the deck. The results

### 2 C. 1 D. 2 4 D. 5 3 C. 25 D. 2

Discrete Math Exam Review Name:. A bag contains oranges, grapefruits, and tangerine. A piece of fruit is chosen from the bag at random. What is the probability that a grapefruit will be chosen from the

### Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes

Worksheet 6 th Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of

### Welcome! U4H2: Worksheet # s 2-7, 9-13, 16, 20. Updates: U4T is 12/12. Announcement: December 16 th is the last day I will accept late work.

Welcome! U4H2: Worksheet # s 2-7, 9-13, 16, 20 Updates: U4T is 12/12 Announcement: December 16 th is the last day I will accept late work. 1 Review U4H1 2 Theoretical Probability 3 Experimental Probability

### Review. Natural Numbers: Whole Numbers: Integers: Rational Numbers: Outline Sec Comparing Rational Numbers

FOUNDATIONS Outline Sec. 3-1 Gallo Name: Date: Review Natural Numbers: Whole Numbers: Integers: Rational Numbers: Comparing Rational Numbers Fractions: A way of representing a division of a whole into

### 1. How to identify the sample space of a probability experiment and how to identify simple events

Statistics Chapter 3 Name: 3.1 Basic Concepts of Probability Learning objectives: 1. How to identify the sample space of a probability experiment and how to identify simple events 2. How to use the Fundamental

### 1. Theoretical probability is what should happen (based on math), while probability is what actually happens.

Name: Date: / / QUIZ DAY! Fill-in-the-Blanks: 1. Theoretical probability is what should happen (based on math), while probability is what actually happens. 2. As the number of trials increase, the experimental

### Math 1342 Exam 2 Review

Math 1342 Exam 2 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) If a sportscaster makes an educated guess as to how well a team will do this

### , x {1, 2, k}, where k > 0. (a) Write down P(X = 2). (1) (b) Show that k = 3. (4) Find E(X). (2) (Total 7 marks)

1. The probability distribution of a discrete random variable X is given by 2 x P(X = x) = 14, x {1, 2, k}, where k > 0. Write down P(X = 2). (1) Show that k = 3. Find E(X). (Total 7 marks) 2. In a game

### Chapter 4: Probability and Counting Rules

Chapter 4: Probability and Counting Rules Before we can move from descriptive statistics to inferential statistics, we need to have some understanding of probability: Ch4: Probability and Counting Rules

### CHAPTER 6 PROBABILITY. Chapter 5 introduced the concepts of z scores and the normal curve. This chapter takes

CHAPTER 6 PROBABILITY Chapter 5 introduced the concepts of z scores and the normal curve. This chapter takes these two concepts a step further and explains their relationship with another statistical concept

### STAT Chapter 14 From Randomness to Probability

STAT 203 - Chapter 14 From Randomness to Probability This is the topic that started my love affair with statistics, although I should mention that we will only skim the surface of Probability. Let me tell

### Independent Events B R Y

. Independent Events Lesson Objectives Understand independent events. Use the multiplication rule and the addition rule of probability to solve problems with independent events. Vocabulary independent

### PROBABILITY. Example 1 The probability of choosing a heart from a deck of cards is given by

Classical Definition of Probability PROBABILITY Probability is the measure of how likely an event is. An experiment is a situation involving chance or probability that leads to results called outcomes.

### Bell Work. Warm-Up Exercises. Two six-sided dice are rolled. Find the probability of each sum or 7

Warm-Up Exercises Two six-sided dice are rolled. Find the probability of each sum. 1. 7 Bell Work 2. 5 or 7 3. You toss a coin 3 times. What is the probability of getting 3 heads? Warm-Up Notes Exercises

### I. WHAT IS PROBABILITY?

C HAPTER 3 PROAILITY Random Experiments I. WHAT IS PROAILITY? The weatherman on 10 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and

### Probability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College

Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical

### Probability of Independent and Dependent Events. CCM2 Unit 6: Probability

Probability of Independent and Dependent Events CCM2 Unit 6: Probability Independent and Dependent Events Independent Events: two events are said to be independent when one event has no affect on the probability

### Unit 9: Probability Assignments

Unit 9: Probability Assignments #1: Basic Probability In each of exercises 1 & 2, find the probability that the spinner shown would land on (a) red, (b) yellow, (c) blue. 1. 2. Y B B Y B R Y Y B R 3. Suppose

### Probability is often written as a simplified fraction, but it can also be written as a decimal or percent.

CHAPTER 1: PROBABILITY 1. Introduction to Probability L EARNING TARGET: I CAN DETERMINE THE PROBABILITY OF AN EVENT. What s the probability of flipping heads on a coin? Theoretically, it is 1/2 1 way to

### Probability --QUESTIONS-- Principles of Math 12 - Probability Practice Exam 1

Probability --QUESTIONS-- Principles of Math - Probability Practice Exam www.math.com Principles of Math : Probability Practice Exam Use this sheet to record your answers:... 4... 4... 4.. 6. 4.. 6. 7..

### Instructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to include your name and student numbers.

Math 3201 Unit 3 Probability Assignment 1 Unit Assignment Name: Part 1 Selected Response: Instructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to

### Probability - Grade 10 *

OpenStax-CNX module: m32623 1 Probability - Grade 10 * Rory Adams Free High School Science Texts Project Sarah Blyth Heather Williams This work is produced by OpenStax-CNX and licensed under the Creative

### MAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability. Preliminary Concepts, Formulas, and Terminology

MAT104: Fundamentals of Mathematics II Summary of Counting Techniques and Probability Preliminary Concepts, Formulas, and Terminology Meanings of Basic Arithmetic Operations in Mathematics Addition: Generally

### When a number cube is rolled once, the possible numbers that could show face up are

C3 Chapter 12 Understanding Probability Essential question: How can you describe the likelihood of an event? Example 1 Likelihood of an Event When a number cube is rolled once, the possible numbers that

### Basic Probability Ideas. Experiment - a situation involving chance or probability that leads to results called outcomes.

Basic Probability Ideas Experiment - a situation involving chance or probability that leads to results called outcomes. Random Experiment the process of observing the outcome of a chance event Simulation

### Advanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY

Advanced Intermediate Algebra Chapter 12 Summary INTRO TO PROBABILITY 1. Jack and Jill do not like washing dishes. They decide to use a random method to select whose turn it is. They put some red and blue

### 2 A fair coin is flipped 8 times. What is the probability of getting more heads than tails? A. 1 2 B E. NOTA

For all questions, answer E. "NOTA" means none of the above answers is correct. Calculator use NO calculators will be permitted on any test other than the Statistics topic test. The word "deck" refers

### Find the probability of an event by using the definition of probability

LESSON 10-1 Probability Lesson Objectives Find the probability of an event by using the definition of probability Vocabulary experiment (p. 522) trial (p. 522) outcome (p. 522) sample space (p. 522) event

### Math 1116 Probability Lecture Monday Wednesday 10:10 11:30

Math 1116 Probability Lecture Monday Wednesday 10:10 11:30 Course Web Page http://www.math.ohio state.edu/~maharry/ Chapter 15 Chances, Probabilities and Odds Objectives To describe an appropriate sample

### MATH-8 SOL8.12 Probability CW Exam not valid for Paper Pencil Test Sessions

MTH- SOL. Probability W Exam not valid for Paper Pencil Test Sessions [Exam I:NFP0 box contains five cards lettered,,,,. If one card is selected at random from the box and NOT replaced, what is the probability

### MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - FALL DR. DAVID BRIDGE

MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - FALL 2009 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the

### MTH 103 H Final Exam. 1. I study and I pass the course is an example of a. (a) conjunction (b) disjunction. (c) conditional (d) connective

MTH 103 H Final Exam Name: 1. I study and I pass the course is an example of a (a) conjunction (b) disjunction (c) conditional (d) connective 2. Which of the following is equivalent to (p q)? (a) p q (b)

### Before giving a formal definition of probability, we explain some terms related to probability.

probability 22 INTRODUCTION In our day-to-day life, we come across statements such as: (i) It may rain today. (ii) Probably Rajesh will top his class. (iii) I doubt she will pass the test. (iv) It is unlikely

### Date. Probability. Chapter

Date Probability Contests, lotteries, and games offer the chance to win just about anything. You can win a cup of coffee. Even better, you can win cars, houses, vacations, or millions of dollars. Games

### ( ) Online MC Practice Quiz KEY Chapter 5: Probability: What Are The Chances?

Online MC Practice Quiz KEY Chapter 5: Probability: What Are The Chances? 1. Research on eating habits of families in a large city produced the following probabilities if a randomly selected household

### Answer each of the following problems. Make sure to show your work.

Answer each of the following problems. Make sure to show your work. 1. A board game requires each player to roll a die. The player with the highest number wins. If a player wants to calculate his or her

### Mathematics 3201 Test (Unit 3) Probability FORMULAES

Mathematics 3201 Test (Unit 3) robability Name: FORMULAES ( ) A B A A B A B ( A) ( B) ( A B) ( A and B) ( A) ( B) art A : lace the letter corresponding to the correct answer to each of the following in

### Conditional Probability Worksheet

Conditional Probability Worksheet EXAMPLE 4. Drug Testing and Conditional Probability Suppose that a company claims it has a test that is 95% effective in determining whether an athlete is using a steroid.

### Georgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Analytic Geometry Unit 7 PRE-ASSESSMENT

PRE-ASSESSMENT Name of Assessment Task: Compound Probability 1. State a definition for each of the following types of probability: A. Independent B. Dependent C. Conditional D. Mutually Exclusive E. Overlapping

### ECON 214 Elements of Statistics for Economists

ECON 214 Elements of Statistics for Economists Session 4 Probability Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education School of Continuing

### Grade 7/8 Math Circles February 25/26, Probability

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Probability Grade 7/8 Math Circles February 25/26, 2014 Probability Centre for Education in Mathematics and Computing Probability is the study of how likely

### Independent and Mutually Exclusive Events

Independent and Mutually Exclusive Events By: OpenStaxCollege Independent and mutually exclusive do not mean the same thing. Independent Events Two events are independent if the following are true: P(A

### Section 11.4: Tree Diagrams, Tables, and Sample Spaces

Section 11.4: Tree Diagrams, Tables, and Sample Spaces Diana Pell Exercise 1. Use a tree diagram to find the sample space for the genders of three children in a family. Exercise 2. (You Try!) A soda machine

### CHAPTERS 14 & 15 PROBABILITY STAT 203

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

### 1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 100 calculators is tested.

1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 0 calculators is tested. Write down the expected number of faulty calculators in the sample. Find

### LC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following.

A Ryan LC OL Probability ARNMaths.weebly.com Learning Outcomes As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. Counting List outcomes of an experiment Apply

### A B C. 142 D. 96

Data Displays and Analysis 1. stem leaf 900 3 3 4 5 7 9 901 1 1 1 2 4 5 6 7 8 8 8 9 9 902 1 3 3 3 4 6 8 9 9 903 1 2 2 3 3 3 4 7 8 9 904 1 1 2 4 5 6 8 8 What is the range of the data shown in the stem-and-leaf

### Total. STAT/MATH 394 A - Autumn Quarter Midterm. Name: Student ID Number: Directions. Complete all questions.

STAT/MATH 9 A - Autumn Quarter 015 - Midterm Name: Student ID Number: Problem 1 5 Total Points Directions. Complete all questions. You may use a scientific calculator during this examination; graphing