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.

Size: px
Start display at page:

Download "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."

Transcription

1 Math 0 Practice Test 3 Fall 2009 Covers 7.5, MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. ) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. ) A) B) 2 C) 0 D) 6 2) If two fair dice are rolled, find the probability of a sum of 5 given that the sum is less than 8. A) 4 2 B) C) D) ) 3) You roll two fair dice. Let E be the event that the sum is even. Let F be the event that a four shows on at least one of the dice. Find P(F E). A) B) C) 7 5 D) ) 4) A box contains 24 blue marbles, 3 green marbles, and 3 red marbles. Two marbles are selected at random without replacement. Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. Find P(F E). A) 3 49 B) 3 50 C) 2 49 D) ) 5) Two marbles are drawn without replacement from a box with blue, 3 white, 2 green, and 2 red marbles. Find the probability that the second marble is red, given that the first marble is white. 3 3 A) B) C) D) ) 6) Suppose one card is selected at random from an ordinary deck of 52 playing cards. Find the probability that the card is a diamond given that it is not a club. 6) A) 3 B) 4 C) D) 0 7) If three cards are drawn without replacement from an ordinary deck, find the probability that the third card is a heart, given that the first two cards were hearts. A) B) 6 C) D) ) Find the probability. 8) Assuming that boy and girl babies are equally likely, find the probability that a family with three children has all boys given that the first two are boys. 8) A) 8 B) 2 C) D) 4

2 9) A family has five children. The probability of having a girl is /2. What is the probability of having 2 girls followed by 3 boys? Round your answer to four decimal places. A) B) C) D) ) 0) Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 5 possible answers. A) B) C) 5 D) ) Find the indicated probability. ) Assume that two marbles are drawn without replacement from a box with blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are green. A) 6 B) 4 C) 28 D) 4 ) Solve the problem. 2) 57% of a store's computers come from factory A and the remainder come from factory B. % of computers from factory A are defective while 4% of computers from factory B are defective. If one of the store's computers is selected at random, what is the probability that it is defective and from factory B? A) B) 0.07 C) 0.47 D) ) 3) 43% of a store's computers come from factory A and the remainder come from factory B. 5% of computers from factory A are defective while % of computers from factory B are defective. If one of the store's computers is selected at random, what is the probability that it is not defective and from factory A? A) 0.95 B) C) D) ) 4) In a certain U.S. city, 5.2% of adults are women. In that city, 4.6% of women and 0.9% of men suffer from depression. If an adult is selected at random from the city, find the probability that the person is a man who does not suffer from depression. A) B) C) 0.89 D) ) 5) In a certain U.S. city, 5.5% of adults are women. In that city, 3.4% of women and 9.6% of men suffer from depression. If an adult is selected at random from the city, find the probability that the person suffers from depression. A) 0.34 B) C) 0.6 D) 0.5 5) 2

3 Use the given table to find the indicated probability. 6) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. 6) Toppings Freshman Sophomore Junior Senior Totals Cheese Meat Veggie A student is selected at random. Find the probability that the student's favorite topping is meat given that the student is a junior. A) B) C) D) ) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. 7) Toppings Freshman Sophomore Junior Senior Totals Cheese Meat Veggie A student is selected at random. Find the probability that the student's favorite topping is veggie given that the student is a junior or senior. A) 0.45 B) 0.64 C) D) ) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. 8) cola root beer lemon-lime totals under 2 years of age between 2 and over 40 years of age One of the participants is selected at random. Find the probability that the person is over 40 and prefers cola. A) C) B) 4 7 D) none of the above 3

4 9) People in a survey were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. 9) cola root beer lemon-lime totals under 2 years of age between 2 and over 40 years of age One of the participants is selected at random. Find the probability that the person is over 40 given that they prefer root beer. A) B) C) D) Evaluate the factorial. 20) 6! A) 20 B) 360 C) 440 D) ) Evaluate the permutation. 2) P(0, 5) A) 720 B) 0 C) 30,240 D) 2) 22) P(25, 5) A) 303,600 B) C) 27,52,000 D) 6,375,600 22) Solve the problem. 23) Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C. In how many ways can a person travel from A to C via B? A) 0 ways B) 36 ways C) 24 ways D) 6 ways 23) 24) In how many ways can 4 people be chosen and arranged in a straight line, if there are 6 people from whom to choose? A) 24 ways B) 360 ways C) 30 ways D) 60 ways 24) 25) License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed? A),757,600 plates B),000,000 plates C) 308,95,776 plates D) 7,576,000 plates 25) 26) A person ordering a certain model of car can choose any of 9 colors, either manual or automatic transmission, and any of 9 audio systems. How many ways are there to order this model of car? A) 62 ways B) 70 ways C) 72 ways D) 58 ways 26) 27) A shirt company has 4 designs that can be made with short or long sleeves. There are 6 color patterns available. How many different types of shirts are available from this company? A) 2 types B) 24 types C) 0 types D) 48 types 27) 28) A restaurant offers 7 possible appetizers, 3 possible main courses, and 6 possible desserts. How many different meals are possible at this restaurant? (Two meals are considered different unless all three courses are the same). A) 546 meals B) 26 meals C) 536 meals D) 343 meals 28) 4

5 How many distinguishable permutations of letters are possible in the word? 29) GIGGLE A) 20 B) 4320 C) 36 D) ) 30) TENNESSEE A) 8 B) 362,880 C) 7560 D) ) 3) COLORADO A) 3,440 B) 6720 C) 4480 D) 40,320 3) Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these could be hired. 32) There is no restriction on the college majors hired for the five positions. 32) A) 24 ways B) 3024 ways C) 5,20 ways D) 20 ways 33) Two accounting majors must be hired first, then one economics major, then two marketing majors. A) 288 ways B) 4 ways C) 44 ways D) 24 ways 33) 34) One accounting major, one economics major, and one marketing major would be hired, then the two remaining positions would be filled by any of the majors left. A) 48 ways B) 4320 ways C) 720 ways D) 260 ways 34) Evaluate the combination ) A) 2 B) 24 C) 24! - 0 D) 24! 35) 36) 7 0 A) 2520 B) 260 C) D) ) 37) 9 A) 9! - 0 B) 9 C) 9! D) 2 37) 38) 3 3 A) 3! - 5 B) C) 2 D) 3! 38) Of the 2,598,960 different five -card hands possible from a deck of 52 playing cards, how many would contain the following cards? 39) No face cards 39) A) 639,730 hands B) 658,008 hands C) 39,865 hands D) 27,946 hands 40) All hearts A) 287 hands B) 43 hands C) 386 hands D) 2574 hands 40) 5

6 4) Two black cards and three red cards A),690,000 hands B),267,500 hands C) 845,000 hands D) 422,500 hands 4) Solve the problem. 42) If you toss five fair coins, in how many ways can you obtain at least one head? A) 6 ways B) 32 ways C) 3 ways D) 5 ways 42) 43) If you toss six fair coins, in how many ways can you obtain at least two heads? A) 58 ways B) 57 ways C) 64 ways D) 63 ways 43) 44) A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many ways can you get 5 apples? A) 24 ways B) 0 ways C) 6 ways D) 2 ways 44) 45) A bag contains 5 apples and 3 oranges. If you select 4 pieces of fruit without looking, how many ways can you get 4 oranges? A) 5 ways B) 5 ways C) 8 ways D) 0 ways 45) Decide whether the situation involves permutations or combinations. 46) A batting order for 9 players for a baseball game. A) Permutation B) Combination 46) 47) A selection of a chairman and a secretary from a committee of 5 people. A) Permutation B) Combination 47) 48) A sample of 0 items taken from 90 items on an assembly line. A) Permutation B) Combination 48) Solve the problem. 49) How many three-digit counting numbers do not contain any of the digits, 5, 7, 8, or 9? A) 00 numbers B) 25 numbers C) 48 numbers D) 64 numbers 49) 50) In how many ways can a group of 6 students be selected from 7 students? A) way B) 6 ways C) 7 ways D) 42 ways 50) 5) How many ways can a committee of 2 be selected from a club with 2 members? A) 2 ways B) 32 ways C) 33 ways D) 66 ways 5) 52) In how many ways can a group of 7 students be selected from 8 students? A) way B) 8 ways C) 56 ways D) 7 ways 52) 53) If the police have 8 suspects, how many different ways can they select 5 for a lineup? A) 336 ways B) 6720 ways C) 56 ways D) 40 ways 53) 54) The chorus has six sopranos and eight baritones. In how many ways can the director choose a quartet that contains at least one soprano? A) 07 ways B) 986 ways C) 00 ways D) 93 ways 54) 6

7 55) A class has 0 boys and 2 girls. In how many ways can a committee of four be selected if the committee can have at most two girls? A) 4620 ways B) 5665 ways C) 570 ways D) 440 ways 55) A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 56) All lemon 56) A) B) 0.22 C) 0.06 D) 0 57) All orange A) B) C) D) ) 58) 2 cherry, lemon A) B) C) 0.22 D) ) 59) cherry, 2 lemon A) B) C) D) ) Find the probability of the following card hands from a 52 -card deck. In poker, aces are either high or low. A bridge hand is made up of 3 cards. 60) In bridge, 6 of one suit, 4 of another, and 3 of another 60) A) B) C) D) ) In bridge, all cards in one suit A) B) C) D) ) In bridge, 4 aces A) B) C) D) ) 62) 63) In bridge, exactly 3 kings and exactly 3 queens A) B) C) D) ) Solve. 64) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 0? A) 8 B) 5 8 C) 3 D) 2 64) 65) In a state lotto you have to pick 4 numbers from to 45. If your numbers match those that the state draws, you win. If you buy 3 tickets, what is your probability of winning? 8 A) B) C) D) ) 66) A lottery game contains 29 balls numbered through 29. What is the probability of choosing a ball numbered 30? A) 29 B) C) 0 D) 29 66) 7

8 Solve the problem. 67) What is the probability that at least 2 of the 435 members of the House of Representatives have the same birthday? A) B) C) D) 67) 68) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 3 from town A and 2 from town B. A) B) C) D) ) 69) At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 2 from town A, 2 from town B, and from town C. A) B) 0.89 C) D) ) 70) A roulette wheel contains 84 slots numbered through 84. The slots,4,7,... are red, the slots 2,5,8,... are green, and the slots 3, 6, 9,... are brown. When the wheel is spun, a ball rolls around the rim and falls into a slot. What is the probability that the ball falls into a green slot? 70) A) 3 B) 2 5 C) 4 D) 2 3 8

9 Answer Key Testname: MATH0 PRACTICETEST3FALL2009 ) C 2) B 3) D 4) C 5) D 6) A 7) A 8) B 9) D 0) A ) C 2) B 3) C 4) D 5) C 6) C 7) C 8) C 9) A 20) D 2) C 22) D 23) C 24) B 25) D 26) A 27) D 28) A 29) A 30) D 3) B 32) C 33) C 34) C 35) B 36) C 37) B 38) B 39) B 40) A 4) C 42) C 43) B 44) C 45) D 46) A 47) A 48) B 49) A 50) C 9

10 Answer Key Testname: MATH0 PRACTICETEST3FALL2009 5) D 52) B 53) C 54) D 55) A 56) D 57) B 58) D 59) C 60) B 6) C 62) C 63) A 64) D 65) D 66) C 67) D 68) A 69) B 70) A 0

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

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

More information

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

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

More information

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions.

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

More information

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

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

More information

Odds: Odds compares the number of favorable outcomes to the number of unfavorable outcomes.

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

More information

Assn , 8.5. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Assn , 8.5. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assn 8.-8.3, 8.5 Name List the outcomes of the sample space. ) There are 3 balls in a hat; one with the number on it, one with the number 6 on it, and one with the number 8 on it. You pick a ball from

More information

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

Chapter 15. Definitions: experiment: is the act of making an observation or taking a measurement. MATH 11008: Probability Chapter 15 Definitions: experiment: is the act of making an observation or taking a measurement. outcome: one of the possible things that can occur as a result of an experiment.

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2. (b) 1.5. (c) 0.5-2.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2. (b) 1.5. (c) 0.5-2. Stats: Test 1 Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given frequency distribution to find the (a) class width. (b) class

More information

A probability experiment is a chance process that leads to well-defined outcomes. 3) What is the difference between an outcome and an event?

A probability experiment is a chance process that leads to well-defined outcomes. 3) What is the difference between an outcome and an event? Ch 4.2 pg.191~(1-10 all), 12 (a, c, e, g), 13, 14, (a, b, c, d, e, h, i, j), 17, 21, 25, 31, 32. 1) What is a probability experiment? A probability experiment is a chance process that leads to well-defined

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Ch. - Problems to look at Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability

More information

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

Example: If we roll a dice and flip a coin, how many outcomes are possible? 12.5 Tree Diagrams Sample space- Sample point- Counting principle- Example: If we roll a dice and flip a coin, how many outcomes are possible? TREE DIAGRAM EXAMPLE: Use a tree diagram to show all the possible

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability that the result

More information

Chapter 6. 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? Ans: 4/52.

Chapter 6. 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? Ans: 4/52. Chapter 6 1. What is the probability that a card chosen from an ordinary deck of 52 cards is an ace? 4/52. 2. What is the probability that a randomly selected integer chosen from the first 100 positive

More information

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

Distributions. and Probability. Find the sample space of an experiment. Find the probability of an event. Sample Space of an Experiment C Probability and Probability Distributions APPENDIX C.1 Probability A1 C.1 Probability Find the sample space of an experiment. Find the probability of an event. Sample Space of an Experiment When assigning

More information

Probability Worksheet

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%

More information

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

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

More information

Grade 7/8 Math Circles Fall 2012 Probability

Grade 7/8 Math Circles Fall 2012 Probability 1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Probability Probability is one of the most prominent uses of mathematics

More information

Chapter 5 - Probability

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

More information

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

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

More information

Fundamentals of 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

More information

Statistics 100A Homework 2 Solutions

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

More information

Hoover High School Math League. Counting and Probability

Hoover High School Math League. Counting and Probability Hoover High School Math League Counting and Probability Problems. At a sandwich shop there are 2 kinds of bread, 5 kinds of cold cuts, 3 kinds of cheese, and 2 kinds of dressing. How many different sandwiches

More information

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 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

More information

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, 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

More information

36 Odds, Expected Value, and Conditional Probability

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

More information

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

Contemporary Mathematics- MAT 130. Probability. a) What is the probability of obtaining a number less than 4? Contemporary Mathematics- MAT 30 Solve the following problems:. A fair die is tossed. What is the probability of obtaining a number less than 4? What is the probability of obtaining a number less than

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups

More information

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

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

More information

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

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

More information

Math 166:505 Fall 2013 Exam 2 - Version A

Math 166:505 Fall 2013 Exam 2 - Version A Name Math 166:505 Fall 2013 Exam 2 - Version A On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work. Signature: Instructions: Part I and II are multiple choice

More information

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

2. How many ways can the letters in PHOENIX be rearranged? 7! = 5,040 ways. Math 142 September 27, 2011 1. How many ways can 9 people be arranged in order? 9! = 362,880 ways 2. How many ways can the letters in PHOENIX be rearranged? 7! = 5,040 ways. 3. The letters in MATH are

More information

Formula for Theoretical Probability

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

More information

AP Stats - Probability Review

AP Stats - Probability Review AP Stats - Probability Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. I toss a penny and observe whether it lands heads up or tails up. Suppose

More information

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

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

More information

Section 6.2 Definition of Probability

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

More information

MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.

MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values. MA 5 Lecture 4 - Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the

More information

Chapter 3: Probability

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

More information

PROBABILITY. Chapter Overview Conditional Probability

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

More information

94 Counting Solutions for Chapter 3. Section 3.2

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

More information

Chapter 6 Review 0 (0.083) (0.917) (0.083) (0.917)

Chapter 6 Review 0 (0.083) (0.917) (0.083) (0.917) Chapter 6 Review MULTIPLE CHOICE. 1. The following table gives the probabilities of various outcomes for a gambling game. Outcome Lose $1 Win $1 Win $2 Probability 0.6 0.25 0.15 What is the player s expected

More information

33 Probability: Some Basic Terms

33 Probability: Some Basic Terms 33 Probability: Some Basic Terms In this and the coming sections we discuss the fundamental concepts of probability at a level at which no previous exposure to the topic is assumed. Probability has been

More information

Name: Date: Use the following to answer questions 2-4:

Name: Date: Use the following to answer questions 2-4: Name: Date: 1. A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event A occurs is recorded. What does this proportion represent? A) The probability

More information

Math 55: Discrete Mathematics

Math 55: Discrete Mathematics Math 55: Discrete Mathematics UC Berkeley, Fall 2011 Homework # 7, due Wedneday, March 14 Happy Pi Day! (If any errors are spotted, please email them to morrison at math dot berkeley dot edu..5.10 A croissant

More information

Introductory Probability. MATH 107: Finite Mathematics University of Louisville. March 5, 2014

Introductory Probability. MATH 107: Finite Mathematics University of Louisville. March 5, 2014 Introductory Probability MATH 07: Finite Mathematics University of Louisville March 5, 204 What is probability? Counting and probability 2 / 3 Probability in our daily lives We see chances, odds, and probabilities

More information

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

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:

More information

1 Combinations, Permutations, and Elementary Probability

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

More information

Most of us would probably believe they are the same, it would not make a difference. But, in fact, they are different. Let s see how.

Most of us would probably believe they are the same, it would not make a difference. But, in fact, they are different. Let s see how. PROBABILITY If someone told you the odds of an event A occurring are 3 to 5 and the probability of another event B occurring was 3/5, which do you think is a better bet? Most of us would probably believe

More information

Chapter 4 - Practice Problems 2

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

More information

MATH 1300: Finite Mathematics EXAM 3 21 April 2015

MATH 1300: Finite Mathematics EXAM 3 21 April 2015 MATH 300: Finite Mathematics EXAM 3 2 April 205 NAME:... SECTION:... INSTRUCTOR:... SCORE Correct (a): /5 = % INSTRUCTIONS. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO BY YOUR ROOM LEADER. All exam pages

More information

Remember to leave your answers as unreduced fractions.

Remember to leave your answers as unreduced fractions. Probability Worksheet 2 NAME: Remember to leave your answers as unreduced fractions. We will work with the example of picking poker cards out of a deck. A poker deck contains four suits: diamonds, hearts,

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Regular smoker

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Regular smoker Exam Chapters 4&5 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A 28-year-old man pays $181 for a one-year

More information

Lecture 13. Understanding Probability and Long-Term Expectations

Lecture 13. Understanding Probability and Long-Term Expectations Lecture 13 Understanding Probability and Long-Term Expectations Thinking Challenge What s the probability of getting a head on the toss of a single fair coin? Use a scale from 0 (no way) to 1 (sure thing).

More information

Combinations and Permutations

Combinations and Permutations Combinations and Permutations What's the Difference? In English we use the word "combination" loosely, without thinking if the order of things is important. In other words: "My fruit salad is a combination

More information

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

Probability --QUESTIONS-- Principles of Math 12 - Probability Practice Exam 1 www.math12.com Probability --QUESTIONS-- Principles of Math - Probability Practice Exam www.math.com Principles of Math : Probability Practice Exam Use this sheet to record your answers:... 4... 4... 4.. 6. 4.. 6. 7..

More information

Counting principle, permutations, combinations, probabilities

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

More information

9.2 The Multiplication Principle, Permutations, and Combinations

9.2 The Multiplication Principle, Permutations, and Combinations 9.2 The Multiplication Principle, Permutations, and Combinations Counting plays a major role in probability. In this section we shall look at special types of counting problems and develop general formulas

More information

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

Basic Probability. Probability: The part of Mathematics devoted to quantify uncertainty AMS 5 PROBABILITY Basic Probability Probability: The part of Mathematics devoted to quantify uncertainty Frequency Theory Bayesian Theory Game: Playing Backgammon. The chance of getting (6,6) is 1/36.

More information

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

Probability (Day 1 and 2) Blue Problems. Independent Events Probability (Day 1 and ) Blue Problems Independent Events 1. There are blue chips and yellow chips in a bag. One chip is drawn from the bag. The chip is placed back into the bag. A second chips is then

More information

Math 1324 Review Questions for Test 2 (by Poage) covers sections 8.3, 8.4, 8.5, 9.1, 9.2, 9.3, 9.4

Math 1324 Review Questions for Test 2 (by Poage) covers sections 8.3, 8.4, 8.5, 9.1, 9.2, 9.3, 9.4 c Dr. Patrice Poage, March 1, 20 1 Math 1324 Review Questions for Test 2 (by Poage) covers sections 8.3, 8.4, 8.5, 9.1, 9.2, 9.3, 9.4 1. A basketball player has a 75% chance of making a free throw. What

More information

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

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

More information

Probability of Compound Events

Probability of Compound Events 1. A jar contains 3 red marbles and 2 black marbles. All the marbles are the same size and there are no other marbles in the jar. On the first selection, a marble is chosen at random and not replaced.

More information

7.5: Conditional Probability

7.5: Conditional Probability 7.5: Conditional Probability Example 1: A survey is done of people making purchases at a gas station: buy drink (D) no drink (Dc) Total Buy drink(d) No drink(d c ) Total Buy Gas (G) 20 15 35 No Gas (G

More information

Fun ways to group students

Fun ways to group students Fun ways to group students Tips for dividing into groups. Picture Cards: Hand out cards with images on such as strawberries, blueberries, blackberries and other such groups of things. Then get them to

More information

AP Statistics 7!3! 6!

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

More information

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

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

More information

Pure Math 30: Explained! 334

Pure Math 30: Explained!  334 www.puremath30.com 334 Lesson 2, Part One: Basic Combinations Basic combinations: In the previous lesson, when using the fundamental counting principal or permutations, the order of items to be arranged

More information

number of equally likely " desired " outcomes numberof " successes " OR

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

More information

Expected Value. 24 February 2014. Expected Value 24 February 2014 1/19

Expected Value. 24 February 2014. Expected Value 24 February 2014 1/19 Expected Value 24 February 2014 Expected Value 24 February 2014 1/19 This week we discuss the notion of expected value and how it applies to probability situations, including the various New Mexico Lottery

More information

COUNTING & PROBABILITY 1

COUNTING & PROBABILITY 1 COUNTING & PROBABILITY 1 1) A restaurant offers 7 entrees and 6 desserts. In how many ways can a person order a two-course meal? 2) In how many ways can a girl choose a two-piece outfit from 5 blouses

More information

MATH Exam 3 Review All material covered in class is eligible for exam, this review is not all inclusive.

MATH Exam 3 Review All material covered in class is eligible for exam, this review is not all inclusive. MATH 132 - Exam 3 Review All material covered in class is eligible for exam, this review is not all inclusive. 1. (6.3) A test consists of ten true-or-false questions. If a student randomly chooses answers

More information

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 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

More information

MAT 1000. Mathematics in Today's World

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

More information

Stats Review Chapters 5-6

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

More information

4.5 Finding Probability Using Tree Diagrams and Outcome Tables

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

More information

Study Guide and Review

Study Guide and Review State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. A tree diagram uses line segments to display possible outcomes. 2. A permutation is an arrangement

More information

5 Week Modular Course in Statistics & Probability Strand 1. Module 3

5 Week Modular Course in Statistics & Probability Strand 1. Module 3 5 Week Modular Course in Statistics & Probability Strand Module JUNIOR CERTIFICATE LEAVING CERTIFICATE. Probability Scale. Relative Frequency. Fundamental Principle of Counting. Outcomes of simple random

More information

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. 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

More information

Chapter 5 A Survey of Probability Concepts

Chapter 5 A Survey of Probability Concepts Chapter 5 A Survey of Probability Concepts True/False 1. Based on a classical approach, the probability of an event is defined as the number of favorable outcomes divided by the total number of possible

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Sample Test 2 Math 1107 DeMaio Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Create a probability model for the random variable. 1) A carnival

More information

8.3 Probability Applications of Counting Principles

8.3 Probability Applications of Counting Principles 8. Probability Applications of Counting Principles In this section, we will see how we can apply the counting principles from the previous two sections in solving probability problems. Many of the probability

More information

Section 7C: The Law of Large Numbers

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

More information

Probability and Compound Events Examples

Probability and Compound Events Examples Probability and Compound Events Examples 1. A compound event consists of two or more simple events. ossing a die is a simple event. ossing two dice is a compound event. he probability of a compound event

More information

I. WHAT IS PROBABILITY?

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

More information

V. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPECTED VALUE

V. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPECTED VALUE V. RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, EXPETED VALUE A game of chance featured at an amusement park is played as follows: You pay $ to play. A penny and a nickel are flipped. You win $ if either

More information

EXAM. Exam #3. Math 1430, Spring 2002. April 21, 2001 ANSWERS

EXAM. Exam #3. Math 1430, Spring 2002. April 21, 2001 ANSWERS EXAM Exam #3 Math 1430, Spring 2002 April 21, 2001 ANSWERS i 60 pts. Problem 1. A city has two newspapers, the Gazette and the Journal. In a survey of 1, 200 residents, 500 read the Journal, 700 read the

More information

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. 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

More information

Using Permutations and Combinations to Compute Probabilities

Using Permutations and Combinations to Compute Probabilities Using Permutations and Combinations to Compute Probabilities Student Outcomes Students distinguish between situations involving combinations and situations involving permutations. Students use permutations

More information

AMS 5 CHANCE VARIABILITY

AMS 5 CHANCE VARIABILITY AMS 5 CHANCE VARIABILITY The Law of Averages When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So if the coin is tossed a large number of times, the number of heads and

More information

The game of roulette is played by throwing a small ball onto a rotating wheel with thirty seven numbered sectors.

The game of roulette is played by throwing a small ball onto a rotating wheel with thirty seven numbered sectors. LIVE ROULETTE The game of roulette is played by throwing a small ball onto a rotating wheel with thirty seven numbered sectors. The ball stops on one of these sectors. The aim of roulette is to predict

More information

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Sample Final Exam Spring 2008 DeMaio Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given degree of confidence and sample data to construct

More information

The overall size of these chance errors is measured by their RMS HALF THE NUMBER OF TOSSES NUMBER OF HEADS MINUS 0 400 800 1200 1600 NUMBER OF TOSSES

The overall size of these chance errors is measured by their RMS HALF THE NUMBER OF TOSSES NUMBER OF HEADS MINUS 0 400 800 1200 1600 NUMBER OF TOSSES INTRODUCTION TO CHANCE VARIABILITY WHAT DOES THE LAW OF AVERAGES SAY? 4 coins were tossed 1600 times each, and the chance error number of heads half the number of tosses was plotted against the number

More information

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 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

More information

High School Statistics and Probability Common Core Sample Test Version 2

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

More information

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

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

More information

Definition and Calculus of Probability

Definition and Calculus of Probability In experiments with multivariate outcome variable, knowledge of the value of one variable may help predict another. For now, the word prediction will mean update the probabilities of events regarding the

More information

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

Math 210. 1. Compute C(1000,2) (a) 499500. (b) 1000000. (c) 2. (d) 999000. (e) None of the above. Math 210 1. Compute C(1000,2) (a) 499500. (b) 1000000. (c) 2. (d) 999000. 2. Suppose that 80% of students taking calculus have previously had a trigonometry course. Of those that did, 75% pass their calculus

More information

Slide 1 Math 1520, Lecture 23. This lecture covers mean, median, mode, odds, and expected value.

Slide 1 Math 1520, Lecture 23. This lecture covers mean, median, mode, odds, and expected value. Slide 1 Math 1520, Lecture 23 This lecture covers mean, median, mode, odds, and expected value. Slide 2 Mean, Median and Mode Mean, Median and mode are 3 concepts used to get a sense of the central tendencies

More information

Exam 1 Review Math 118 All Sections

Exam 1 Review Math 118 All Sections Exam Review Math 8 All Sections This exam will cover sections.-.6 and 2.-2.3 of the textbook. No books, notes, calculators or other aids are allowed on this exam. There is no time limit. It will consist

More information

The number of phone calls to the attendance office of a high school on any given school day A) continuous B) discrete

The number of phone calls to the attendance office of a high school on any given school day A) continuous B) discrete Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) State whether the variable is discrete or continuous.

More information

Binomial random variables (Review)

Binomial random variables (Review) Poisson / Empirical Rule Approximations / Hypergeometric Solutions STAT-UB.3 Statistics for Business Control and Regression Models Binomial random variables (Review. Suppose that you are rolling a die

More information