# Probability Review 41

Size: px
Start display at page:

Transcription

1 Probability Review 41 For the following problems, give the probability to four decimals, or give a fraction, or if necessary, use scientific notation. Use P(A) = 1 - P(not A) 1) A coin is tossed 6 times. Find the probability of getting at least 1 head. 2) What is the probability that a 3 letter word contains at least 1 b? 3) What is the probability that a 5 digit number has at least 1 odd digit? Number Problems 4) Find the probabilities. a) A two digit number contains only the digits 5, 6, and 7. b) A three digit number contains the digits 4, 5, and 6. c) A four digit number contains only the digits 1 and 2. d) A three digit number is > 799 and contains the digits 8, 9, and 0. e) A three digit number contains at least one 5. f) A three digit number contains exactly two 5 s. g) A four digit number contains only even digits. h) A three digit number has digits that are all different. Dice Problems 5) Two dice are rolled. Find the probabilities.

2 a) P(at least one 6) b) P(sum > 9) 6) Three dice are rolled. Find the probabilities. a) P(three 6 s) b) P(one 6) c) P(at least one 6) d) P(two 3 s) e) P(no 5) f) P(three different numbers) 7) Four dice are rolled. Find the probabilities. a) P(three 6 s) b) P(two 6 s) Coin Problems 8) A coin is tossed 7 times. Find the probabilities. a) P(no heads) b) P(at least one head) c) P(three heads) c) P(at least 5 heads) Marble Problems 9) A jar contains 3 red, 2 blue, and 4 green marbles. a) Pick one marble. Find P(red) b) Pick one marble. Find P(red or blue) c) Pick one marble, then replace it. Find P(blue then green) 10) One jar contains 2 white marbles and 4 black marbles. Another jar contains 1 white marble and 3 black marbles. One marble is drawn from each jar. Find the probabilities.

3 a) P(two black) b) P(one black and one white) One marble is picked from one of the jars. Find the probabilities (use a tree diagram). c) P(white) d) P(black) 11) A jar contains 4 black and 3 white marbles. Two marbles are picked. Find the probabilities. a) P(W and W) b) P(B and B) c) P(B and W any order) 12) A jar contains 3 red, 5 blue and 6 yellow marbles. Pick three marbles. Find the probabilities. a) P(3 red) b) P(2 blue, 1 yellow) c) P(3 yellow) Binomial Problems 13) The probability of winning a game is Find the following probabilities if four games are played. a) P(1 win) b) P(2 wins) c) P(4 wins) 14) Five dice are rolled. Find the probabilities. a) P(one 4) b) P(two 5 s) c) P(at least three 2 s) 15) Suppose that 30 coins are tossed. Find the probability of getting 18 heads. 16) A survey was taken in a large town. It was found that 70% of people like cats, and 30% of people hate cats. Use the binomial distribution to find the

4 probability that 8 people will like cats in a random selection of 12 people. Conditional Probabilities 17) A card is drawn from a deck. Find the following conditional probabilities. a) The card is a heart, given that it is not a diamond. b) The card is a heart, given that it is a face card. c) The card is a face card, given that it is a club. d) The card is a king, given that it is a club or a spade. 18) The probability that a battery lasts one year is 0.8. The probability that it lasts two years is 0.5. If the battery lasts one year, give the probability that it will last two years. Card Problems 19)a) A card is dealt from a shuffled deck. It is not known. What is the probability that the next card dealt will be black? b) A red card is dealt from a shuffled deck. What is the probability that the next card will be black? 20) Two cards are dealt from a shuffled deck. Find the probabilities. a) P(two red) b) P(two kings) c) P(one red, one black) d) P(one club) e) P(two clubs) f) P(no clubs) 21) Five cards are dealt from a deck. Find the probabilities. a) P(ace of diamonds)

5 b) P(2 hearts and 3 spades) c) P(4 kings) 22) Five cards (a poker hand) are dealt from a shuffled deck. Find the probabilities. a) P(royal flush) b) P(straight flush, includes royal flush) c) P(flush, includes straight flush and royal flush) d) P(four of a kind) e) P(full house) f) P(three of a kind, including full house) g) P(straight, including straight flushes) h) P(two pair) Bayes Theorem 23) Jar 1 contains two red and three green marbles. Jar 2 contains three red and four green marbles. A marble is picked from one of the jars. It is red. What is the probability that the ball came from jar 1? 24) Al and Bob work on an assembly line making computers. Al produces 60% of the computers and does unsatisfactory work 8% of the time. Bob produces 40% of the computers and does unsatisfactory work 5% of the time. A computer at the end of the line is picked at random. Find the probabilities. a) Find the probability that the computer has had unsatisfactory work done on it. b) What is the probability that Al worked on the computer if it is

6 unsatisfactory. c) What is the probability that Bob worked on the computer if the work is satisfactory. Other Problems 25) What is the probability that a 3 digit number does not contain a five? 26) What is the probability that a card dealt from a deck, is a three, a heart, or a face card? 27) In a certain town, a survey shows that 80% of the people own a house, 90% of the people own a car, and 75% own both a car and a house. Find the probabilities. a) P(a person does not own a house or a car) b) P(a person owns a car but not a house) c) P(a person owns a car or a house) 28) Three boys, Allan, Bob and Carl, write their names on three cards. The cards are placed in a hat. Each then picks a card. Find the probabilities. a) Each picks the card with their name. b) Each picks a card that doesn t have their name. c) Only one of the boys picks a card with their name. 29) Seven cards are numbered from 1 to 7, and put in a box. Two cards are picked. Find the probabilities. a) P(two odds) b) P(one odd) c) P(sum > 8) 30) In a shipment of 200 computer chips, 8 are known to be defective. If 10 of the chips are picked at random, what is the probability that 2 of the chips

7 are defective? 31) Three cards are dealt from a shuffled deck. What is the probability of getting the ace of hearts? 32) On a multiple choice test, John guesses the answers. There are 10 questions. Each question has 4 possible answers. Find the probability that John answers five questions correctly and just passes the test. Use the binomial theorem. 33) Find the probability of picking the right combination of a lock. There are 40 different numbers. Three different numbers must be chosen. 34) In a shop, machine A works 80% of the time. Machine B works 70% of the time. Find the probabilities. a) Both machines do not work. b) Both machines do work. c) Only one of the machines works. 35) John has two job interviews. He thinks the chance of getting job A is 0.6, and the chance of getting job B is 0.7. Draw a Venn diagram to find the probabilities. a) P(two job offers) b) P(no job offer) c) P(one job offer) 36) A teacher chooses two students from a class of 10 to do a project. What is the probability that Robert is chosen, but John is not chosen? 37) A bridge hand consists of 13 cards. Find the probability of getting exactly seven diamonds. Answers: 1) , 2) , 3) , 4)a) , b) , c) , d) , e) , f) , g) , h) , 5)a) , b) , 6)a) , b) , c) , d) , e) , f) , 7)a) , b) , 8)a) , b) , c) , d) , 9)a) , b) , c) , 10)a) , b) , c)

8 0.2917, d) , 11)a) , b) , c) , 12)a) , b) , c) , 13)a) , b) , c) , 14)a) , b) , c) , 15) , 16) , 17)a) , b) , c) , d) , 18) , 19)a) , b) , 20)a) , b) , c) , d) , e) , f) , 21)a) , b) , c) 1.847x10-5, 22) (H = 52 C 5 ), a) 4/H = 1.539x10-6, b) 4x10/H = 1.539x10-5, c) 4x 13 C 5 /H = , d) 13x48/H = 2.401x10-4, e) 13x 4 C 3 x 4 C 2 x12/h = 1.441x10-3, f) 13x 4 C 3 x 48 C 2 /H = 2.257x10-2, g) 10x4 5 /H = , h) 44x( 4 C 2 ) 2 x 13 C 2 /H = , 23) , 24)a) , b) , c) , 25) , 26) , 27)a) , b) , c) , 28)a) 1/6, b) 1/3, c) 1/2, 29)a) 2/7, b) 4/7, c) 3/7, 30) [ 8 C 2 x 192 C 8 / 200 C 10 ] = , 31) 1x 51 C 2 / 52 C 3 = 3/52 = , 32) , 33) 1.687x10-5, 34)a) , b) , c) )a) 0.42, b) 0.12, c) 0.46, 36) 8/45, 37) , 38) Choose the other door, because your chances of winning will be 1/2. If you stick with your first choice, your chances of winning are 1/3.

### 1MA01: Probability. Sinéad Ryan. November 12, 2013 TCD

1MA01: Probability Sinéad Ryan TCD November 12, 2013 Definitions and Notation EVENT: a set possible outcomes of an experiment. Eg flipping a coin is the experiment, landing on heads is the event If an

### Lesson 16.1 Assignment

Lesson 16.1 Assignment Name Date Rolling, Rolling, Rolling... Defining and Representing Probability 1. Rasheed is getting dressed in the dark. He reaches into his sock drawer to get a pair of socks. He

### 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

### Unit 7 Central Tendency and Probability

Name: Block: 7.1 Central Tendency 7.2 Introduction to Probability 7.3 Independent Events 7.4 Dependent Events 7.1 Central Tendency A central tendency is a central or value in a data set. We will look at

### Unit 1 Day 1: Sample Spaces and Subsets. Define: Sample Space. Define: Intersection of two sets (A B) Define: Union of two sets (A B)

Unit 1 Day 1: Sample Spaces and Subsets Students will be able to (SWBAT) describe events as subsets of sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,

### 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:

### 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

### 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

### Conditional Probability Worksheet

Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 3-6, compute the conditional probabilities P( AB) and P( B A ) 3. P A = 0.7, P B = 0.4, P A B = 0.25 4. P A = 0.45, P B = 0.8, P A

### 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.

### 0-5 Adding Probabilities. 1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins.

1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins. d. a. Copy the table and add a column to show the experimental probability of the spinner landing on

### These Probability NOTES Belong to:

hese Probability NOES elong to: Date opic Notes Questions. Intro 2. And & Or 3. Dependant & Independent. Dependant & Independent 5. Conditional 6. Conditional 7. Combinations & Permutations 8. inomial

### Compound Probability. Set Theory. Basic Definitions

Compound Probability Set Theory A probability measure P is a function that maps subsets of the state space Ω to numbers in the interval [0, 1]. In order to study these functions, we need to know some basic

### 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

### 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

### MATH 1115, Mathematics for Commerce WINTER 2011 Toby Kenney Homework Sheet 6 Model Solutions

MATH, Mathematics for Commerce WINTER 0 Toby Kenney Homework Sheet Model Solutions. A company has two machines for producing a product. The first machine produces defective products % of the time. The

### 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

### , -the of all of a probability experiment. consists of outcomes. (b) List the elements of the event consisting of a number that is greater than 4.

4-1 Sample Spaces and Probability as a general concept can be defined as the chance of an event occurring. In addition to being used in games of chance, probability is used in the fields of,, and forecasting,

### April 10, ex) Draw a tree diagram of this situation.

April 10, 2014 12-1 Fundamental Counting Principle & Multiplying Probabilities 1. Outcome - the result of a single trial. 2. Sample Space - the set of all possible outcomes 3. Independent Events - when

### Lesson 3 Dependent and Independent Events

Lesson 3 Dependent and Independent Events When working with 2 separate events, we must first consider if the first event affects the second event. Situation 1 Situation 2 Drawing two cards from a deck

### 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 CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE

MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING 2009 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the

### Practice 9-1. Probability

Practice 9-1 Probability You spin a spinner numbered 1 through 10. Each outcome is equally likely. Find the probabilities below as a fraction, decimal, and percent. 1. P(9) 2. P(even) 3. P(number 4. P(multiple

### 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

### Today s Topics. Next week: Conditional Probability

Today s Topics 2 Last time: Combinations Permutations Group Assignment TODAY: Probability! Sample Spaces and Event Spaces Axioms of Probability Lots of Examples Next week: Conditional Probability Sets

### Section 7.3 and 7.4 Probability of Independent Events

Section 7.3 and 7.4 Probability of Independent Events Grade 7 Review Two or more events are independent when one event does not affect the outcome of the other event(s). For example, flipping a coin and

### More Probability: Poker Hands and some issues in Counting

More Probability: Poker Hands and some issues in Counting Data From Thursday Everybody flipped a pair of coins and recorded how many times they got two heads, two tails, or one of each. We saw that the

### Probability Worksheet Yr 11 Maths B Term 4

Probability Worksheet Yr Maths B Term A die is rolled. What is the probability that the number is an odd number or a? P(odd ) Pr(odd or a + 6 6 6 A set of cards is numbered {,, 6}. A card is selected at

### 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

### Math 227 Elementary Statistics. Bluman 5 th edition

Math 227 Elementary Statistics Bluman 5 th edition CHAPTER 4 Probability and Counting Rules 2 Objectives Determine sample spaces and find the probability of an event using classical probability or empirical

### b) Find the exact probability of seeing both heads and tails in three tosses of a fair coin. (Theoretical Probability)

Math 1351 Activity 2(Chapter 11)(Due by EOC Mar. 26) Group # 1. A fair coin is tossed three times, and we would like to know the probability of getting both a heads and tails to occur. Here are the results

### 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

### Section 6.5 Conditional Probability

Section 6.5 Conditional Probability Example 1: An urn contains 5 green marbles and 7 black marbles. Two marbles are drawn in succession and without replacement from the urn. a) What is the probability

### 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.

### 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

### 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

### CONDITIONAL PROBABILITY Assignment

State which the following events are independent and which are dependent.. Drawing a card from a standard deck of playing card and flipping a penny 2. Drawing two disks from an jar without replacement

### C) 1 4. Find the indicated probability. 2) A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

Chapter Probability Practice STA03, Broward College Answer the question. ) On a multiple choice test with four possible answers (like this question), what is the probability of answering a question correctly

### Compound Probability. A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events.

Probability 68B A to determine the likelihood of two events occurring at the. ***Events can be classified as independent or dependent events. Independent Events are events in which the result of event

### 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

### Here are two situations involving chance:

Obstacle Courses 1. Introduction. Here are two situations involving chance: (i) Someone rolls a die three times. (People usually roll dice in pairs, so dice is more common than die, the singular form.)

### Name: Section: Date:

WORKSHEET 5: PROBABILITY Name: Section: Date: Answer the following problems and show computations on the blank spaces provided. 1. In a class there are 14 boys and 16 girls. What is the probability of

### Quiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II??

Quiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II?? Some things to Know, Memorize, AND Understand how to use are n What are the formulas? Pr ncr Fill in the notation

### Important Distributions 7/17/2006

Important Distributions 7/17/2006 Discrete Uniform Distribution All outcomes of an experiment are equally likely. If X is a random variable which represents the outcome of an experiment of this type, then

### GSE Honors Geometry. 1. Create a lattice diagram representing the possible outcomes for the two tiles

GSE Honors Geometry Unit 9 Applications of Probability Name Unit Test Review Part 1 You and a friend have made up a game that involves drawing one numbered tile out of each of two separate bags. The first

### Use Venn diagrams to determine whether the following statements are equal for all sets A and B. 2) A' B', A B Answer: not equal

Test Prep Name Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z} Determine the following. ) (A' C) B' {r, t, v, w, x} Use Venn diagrams to determine whether

### Chapter 8: Probability: The Mathematics of Chance

Chapter 8: Probability: The Mathematics of Chance Free-Response 1. A spinner with regions numbered 1 to 4 is spun and a coin is tossed. Both the number spun and whether the coin lands heads or tails is

### Lesson Lesson 3.7 ~ Theoretical Probability

Theoretical Probability Lesson.7 EXPLORE! sum of two number cubes Step : Copy and complete the chart below. It shows the possible outcomes of one number cube across the top, and a second down the left

### Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together.

Required Probability = where Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together. Solution: As girls are always together so they are considered as a group.

### STAT Statistics I Midterm Exam One. Good Luck!

STAT 515 - Statistics I Midterm Exam One Name: Instruction: You can use a calculator that has no connection to the Internet. Books, notes, cellphones, and computers are NOT allowed in the test. There are

### Essential Question How can you list the possible outcomes in the sample space of an experiment?

. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G..B Sample Spaces and Probability Essential Question How can you list the possible outcomes in the sample space of an experiment? The sample space of an experiment

### 2.5 Sample Spaces Having Equally Likely Outcomes

Sample Spaces Having Equally Likely Outcomes 3 Sample Spaces Having Equally Likely Outcomes Recall that we had a simple example (fair dice) before on equally-likely sample spaces Since they will appear

### 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

### Poker: Further Issues in Probability. Poker I 1/29

Poker: Further Issues in Probability Poker I 1/29 How to Succeed at Poker (3 easy steps) 1 Learn how to calculate complex probabilities and/or memorize lots and lots of poker-related probabilities. 2 Take

### Section Introduction to Sets

Section 1.1 - Introduction to Sets Definition: A set is a well-defined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase

### Statistics and Probability

Lesson Statistics and Probability Name Use Centimeter Cubes to represent votes from a subgroup of a larger population. In the sample shown, the red cubes are modeled by the dark cubes and represent a yes

### Probability Quiz Review Sections

CP1 Math 2 Unit 9: Probability: Day 7/8 Topic Outline: Probability Quiz Review Sections 5.02-5.04 Name A probability cannot exceed 1. We express probability as a fraction, decimal, or percent. Probabilities

### Revision 6: Similar Triangles and Probability

Revision 6: Similar Triangles and Probability Name: lass: ate: Mark / 52 % 1) Find the missing length, x, in triangle below 5 cm 6 cm 15 cm 21 cm F 2) Find the missing length, x, in triangle F below 5

### 6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices?

Pre-Calculus Section 4.1 Multiplication, Addition, and Complement 1. Evaluate each of the following: a. 5! b. 6! c. 7! d. 0! 2. Evaluate each of the following: a. 10! b. 20! 9! 18! 3. In how many different

### Algebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations

Algebra 2 Notes Section 10.1: Apply the Counting Principle and Permutations Objective(s): Vocabulary: I. Fundamental Counting Principle: Two Events: Three or more Events: II. Permutation: (top of p. 684)

### Honors Precalculus Chapter 9 Summary Basic Combinatorics

Honors Precalculus Chapter 9 Summary Basic Combinatorics A. Factorial: n! means 0! = Why? B. Counting principle: 1. How many different ways can a license plate be formed a) if 7 letters are used and each

### Probability - Chapter 4

Probability - Chapter 4 In this chapter, you will learn about probability its meaning, how it is computed, and how to evaluate it in terms of the likelihood of an event actually happening. A cynical person

### Objectives. Determine whether events are independent or dependent. Find the probability of independent and dependent events.

Objectives Determine whether events are independent or dependent. Find the probability of independent and dependent events. independent events dependent events conditional probability Vocabulary Events

### Section 7.1 Experiments, Sample Spaces, and Events

Section 7.1 Experiments, Sample Spaces, and Events Experiments An experiment is an activity with observable results. 1. Which of the follow are experiments? (a) Going into a room and turning on a light.

### 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

### Foundations to Algebra In Class: Investigating Probability

Foundations to Algebra In Class: Investigating Probability Name Date How can I use probability to make predictions? Have you ever tried to predict which football team will win a big game? If so, you probably

### 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

### 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.

### ALL FRACTIONS SHOULD BE IN SIMPLEST TERMS

Math 7 Probability Test Review Name: Date Hour Directions: Read each question carefully. Answer each question completely. ALL FRACTIONS SHOULD BE IN SIMPLEST TERMS! Show all your work for full credit!

### Chapter-wise questions. Probability. 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail.

Probability 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail. 2. 26 cards marked with English letters A to Z (one letter on each card) are shuffled well. If one

### 6) A) both; happy B) neither; not happy C) one; happy D) one; not happy

MATH 00 -- PRACTICE TEST 2 Millersville University, Spring 202 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all natural

### STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving.

Worksheet 4 th Topic : PROBABILITY TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving. BASIC COMPETENCY:

### UNIT 4 APPLICATIONS OF PROBABILITY Lesson 1: Events. Instruction. Guided Practice Example 1

Guided Practice Example 1 Bobbi tosses a coin 3 times. What is the probability that she gets exactly 2 heads? Write your answer as a fraction, as a decimal, and as a percent. Sample space = {HHH, HHT,

### Class XII Chapter 13 Probability Maths. Exercise 13.1

Exercise 13.1 Question 1: Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E F) = 0.2, find P (E F) and P(F E). It is given that P(E) = 0.6, P(F) = 0.3, and P(E F) = 0.2 Question 2:

### If you roll a die, what is the probability you get a four OR a five? What is the General Education Statistics

If you roll a die, what is the probability you get a four OR a five? What is the General Education Statistics probability that you get neither? Class Notes The Addition Rule (for OR events) and Complements

### Exam 2 Review (Sections Covered: 3.1, 3.3, , 7.1) 1. Write a system of linear inequalities that describes the shaded region.

Exam 2 Review (Sections Covered: 3.1, 3.3, 6.1-6.4, 7.1) 1. Write a system of linear inequalities that describes the shaded region. 5x + 2y 30 x + 2y 12 x 0 y 0 2. Write a system of linear inequalities

### MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE

MATH 205 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM # - SPRING 2006 - DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Tell whether the statement is

### The point value of each problem is in the left-hand margin. You must show your work to receive any credit, except on problems 1 & 2. Work neatly.

Introduction to Statistics Math 1040 Sample Exam II Chapters 5-7 4 Problem Pages 4 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of

### Enrichment. Suppose that you are given this information about rolling a number cube.

ate - Working ackward with Probabilities Suppose that you are given this information about rolling a number cube. P() P() P() an you tell what numbers are marked on the faces of the cube Work backward.

### CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY

CHAPTER 9 - COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many real-world fields, such as insurance, medical research, law enforcement, and political science. Objectives:

### 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:

### Week in Review #5 ( , 3.1)

Math 166 Week-in-Review - S. Nite 10/6/2012 Page 1 of 5 Week in Review #5 (2.3-2.4, 3.1) n( E) In general, the probability of an event is P ( E) =. n( S) Distinguishable Permutations Given a set of n objects

### 6/24/14. The Poker Manipulation. The Counting Principle. MAFS.912.S-IC.1: Understand and evaluate random processes underlying statistical experiments

The Poker Manipulation Unit 5 Probability 6/24/14 Algebra 1 Ins1tute 1 6/24/14 Algebra 1 Ins1tute 2 MAFS. 7.SP.3: Investigate chance processes and develop, use, and evaluate probability models MAFS. 7.SP.3:

### 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

### Section 5.4 Permutations and Combinations

Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to

### Probability Review before Quiz. Unit 6 Day 6 Probability

Probability Review before Quiz Unit 6 Day 6 Probability Warm-up: Day 6 1. A committee is to be formed consisting of 1 freshman, 1 sophomore, 2 juniors, and 2 seniors. How many ways can this committee be

### Exam 2 Review F09 O Brien. Finite Mathematics Exam 2 Review

Finite Mathematics Exam Review Approximately 5 0% of the questions on Exam will come from Chapters, 4, and 5. The remaining 70 75% will come from Chapter 7. To help you prepare for the first part of the

### Probability and the Monty Hall Problem Rong Huang January 10, 2016

Probability and the Monty Hall Problem Rong Huang January 10, 2016 Warm-up: There is a sequence of number: 1, 2, 4, 8, 16, 32, 64, How does this sequence work? How do you get the next number from the previous

### 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

### STAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes

STAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes Pengyuan (Penelope) Wang May 25, 2011 Review We have discussed counting techniques in Chapter 1. (Principle

### Poker: Probabilities of the Various Hands

Poker: Probabilities of the Various Hands 22 February 2012 Poker II 22 February 2012 1/27 Some Review from Monday There are 4 suits and 13 values. The suits are Spades Hearts Diamonds Clubs There are 13

### 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

### NC MATH 2 NCFE FINAL EXAM REVIEW Unit 6 Probability

NC MATH 2 NCFE FINAL EXAM REVIEW Unit 6 Probability Theoretical Probability A tube of sweets contains 20 red candies, 8 blue candies, 8 green candies and 4 orange candies. If a sweet is taken at random

### MATH STUDENT BOOK. 7th Grade Unit 6

MATH STUDENT BOOK 7th Grade Unit 6 Unit 6 Probability and Graphing Math 706 Probability and Graphing Introduction 3 1. Probability 5 Theoretical Probability 5 Experimental Probability 13 Sample Space 20

### A Probability Work Sheet

A Probability Work Sheet October 19, 2006 Introduction: Rolling a Die Suppose Geoff is given a fair six-sided die, which he rolls. What are the chances he rolls a six? In order to solve this problem, we

### Define and Diagram Outcomes (Subsets) of the Sample Space (Universal Set)

12.3 and 12.4 Notes Geometry 1 Diagramming the Sample Space using Venn Diagrams A sample space represents all things that could occur for a given event. In set theory language this would be known as the

### Section 5.4 Permutations and Combinations

Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! = n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to

### 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