6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices?
|
|
- Cornelia Stevens
- 5 years ago
- Views:
Transcription
1 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 ways can your arrange five books on a shelf? 4. In how many different ways can nine people be arranged in a line? 5. In how many different ways can you answer 10 true-false questions? 6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices? 7. Many radio stations have 4-letter call signs beginning with K. How many such call signs are possible if: a. letters can be repeated? b. letters cannot be repeated? 8. How many 3-digit numbers can be formed using the digits 4, 5, 6, 7, 8 if: a. the digits can be repeated? b. the digits cannot be repeated? 9. In how many ways can four people be seated in a row of 12 chairs? 10. In how many ways can four different prizes be given to any four of ten people if no person receives more than one prize? 11. Four cards numbered 1 through 4 are shuffled and three different cards are chosen one at a time. How many ways can this be done? 12. A high school coach must decide on the batting order for a baseball team of nine players. a. How many different batting orders are possible? b. How many different batting orders are possible if the pitcher bats last? c. How many different batting orders are possible if the pitcher bats last and the team s best hitter bats third? 13. A track coach must choose a 4-person 400 m relay team and a 4-person 800 m relay team from a squad of seven sprinters, any of whom can run on either team. If the fastest sprinter runs last in both races, in how many ways can the coach form the two teams if each of the six remaining sprinters runs only once and each different order is counted as a different team? 14. How many numbers consisting of one, two or three digits (without repetitions) can be formed using the digits 1, 2, 3, 4, 5, 6? 15. If you have five signal flags and can send messages by hoisting one or more flags on a flagpole, how many messages can you send? 16. In some states license plates consist of three letters followed by two or three digitis (for example, RRK54 or ABC055). How many such possibilities are there for: a. those plates with two digits? b. those plates with three digits? c. In all, how many license plates are possible? 17. How many possibilities are there for a license plate with two letters and three or four non-zero digits? 18. a. How many three-digit numbers contain no 7 s? b. How many three-digit numbers contain at least one 7?
2 19. a. How many four-digit numbers contain no 8 s or 9 s? b. How many four-digit numbers contain at least one 8 or 9? 20. How many numbers from 5000 to 6999 contain at least one 3? 21. Many license plates in the U.S. consist of three letters followed by a three-digit number from 100 to 999. How many of these contain at least one of the vowels A, E, I, O, and U? 22. Telephone numbers in the U.S. and Canada have 10 digits as follows: Three-digit area code number: first digit is not 0 or 1 Second digit must be 0 or 1 Three-digit exchange number: first and second digits are not 0 or 1 Four-digit line number not all zeros a. How many possible area codes are there? b. The area code for Frankfort is 815. Within this area code how many exchange numbers are possible? c. The area code for Tinley Park is 708. Within this exchange, how many line numbers are possible? d. How many seven-digit phone numbers are possible in the 815 area code? e. How many ten-digit phone numbers are possible in the U.S. and Canada? f. Suppose a state has five telephone area codes. How many phone numbers could there be in the state without adding any more area codes? 23. a. How many nine-letter words can be formed using the letters of the word FISHERMAN? b. How many nine-letter words begin and end with a vowel? 24. Suppose the letters of VERMONT are used to form words. a. How many seven-letter words can be formed? b. How many six-letter words can be formed? c. how many five letter words can be formed which begin with a vowel and end with a consonant? Pre-Calculus Section 4.2 Permutations and Combinations 1. a. In how many ways can a club with 20 members choose a president and a vice-president? b. In how many ways can the club choose a two-person governing council? 2. a. In how many ways can a club with 13 members choose four different officers? b. In how many ways can the club choose a four-person governing council? 3. a. In how many ways can a host-couple choose four couples to invite for dinner from a group of ten couples? b. Ten students each submit a woodworking project in an industrial arts competition. There is to be a first-place prize, a second-place prize, a third-place prize, and an honorable mention. In how many ways can these awards be presented? 4. A teach has a collection of 20 true-false questions and wishes to choose five of them for a quiz. How many quizzes can be made if: a. the order of the questions on the quiz is important? b. the order of the questions on the quiz is unimportant? 5. Each of the 200 students attending a school dance has a ticket with a number for a door prize. If three different numbers are selected, how many ways are there to award the prizes: a. given that the prizes are identical? b. given that the prizes are different? 6. Suppose you bought four books and gave one to each of four friends. In how many ways can the books be given if: a. they are all different? b. they are all identical? 7. Eight people apply for three job positions. In how many different ways can the three positions be filled if: a. the positions are all different? b. the positions are all the same?
3 8. How many different ways are there to deal a hand of five cards from a standard deck of 52 cards if: a. the order in which the cards are dealt is important? b. the order in which the cards are dealt is not important? 9. In how many ways can six hockey players be chosen from a group of twelve if: a. the playing positions are considered? b. the playing positions are not considered? 10. Of the twelve players on a school s basketball team, the coach must choose five players to be in the starting lineup. In how many ways can this be done if: a. the playing positions are considered? b. the playing positions are not considered? 11. a. A hiker would like to invite seven friends to go on a trip but has room for only four of them. In how many ways can they be chosen? b. If there were room for only three friends, in how many ways could they be chosen? 12. a. In how many ways can you choose three letters from the word LOGARITHM if the order of the letters is unimportant? b. In how many ways can you choose six letters from the word LOGARITHM if the order of the letters is unimportant? 13. A certain chain of ice cream stores sells 28 different flavors, and a customer can order a single-scoop, double-scoop, or triple-scoop cone. Suppose on a multi-scoop cone that the order of the flavors is important and that the flavors can be repeated. How many possible cones are there? 14. Three couples go to the movies and sit together in a row of six seats. In how many ways can these people arrange themselves if each couple sits together? 15. A math teacher uses four algebra books, two geometry books, and three pre-calculus books for reference. In how many ways can the teacher arrange the books on a shelf if books covering the same subject matter are kept together? Pre-Calculus Section 4.3 Introduction to Probability 1. Suppose a card is drawn from a well-shuffled standard deck of 52 cards. Find the probability of drawing each of the following: a. a black card b. a spade c. not a spade d. a black face card e. a black jack f. not a black jack g. a red diamond h. a black diamond i. not a black diamond j. a jack k. a jack or king l. neither a jack nor a king 2. Mr. and Mrs. Smith each bought ten raffle tickets. Each of their three children bought four tickets. If 4280 tickets were sold in all, what is the probability that the grand prize winner is: a. Mr. or Mrs. Smith? b. one of the 5 Smiths? c. none of the Smiths? 3. One of the integers between 11 and 20 inclusive, is picked at random. What is the probability that: a. the integer is even? b. the integer is divisible by 3? c. the integer is prime? 4. Two fair dice are rolled. Find the probability that: a. the sum is 6. b. the sum is 7. c. the sum is 8. d. the sum is even e. the sum is 12. f. the sum is less than 12. g. the two dice show different numbers h. the red die shows a greater number than the white die. 5. A die is rolled and a coin is tossed. Find the probability that the die s number is even and the coin is heads. 6. The numbers 1, 2, 3, and 4 are written on separate slips of paper and placed in a hat. Two slips of paper are then randomly drawn, one after the other and without replacement. Find the probability that the sum of the numbers picked is 6 or more.
4 7. Suppose that the odds in favor of the National League s winning the All-Star Gram are 4:3. a. What is the probability that the National League wins? b. What is the probability that the American League wins? 8. Suppose that the odds in favor of the incumbent s winning an election are 2:3. a. What is the probability that the incumbent wins? b. What is the probability that the incumbent s challenger wins? 9. Suppose you roll two dice, each of which is a regular octahedron with faces numbered 1 to 8. a. What is the probability that the sum of the numbers showing is 2? b. What is the probability that the sum of the numbers showing is 3? c. What sum is most likely to appear? 10. Suppose you roll two dice, each of which is a regular dodecahedron with faces numbered 1 to 12. a. What is the probability that the sum of the numbers showing is 24? b. What is the probability that the sum is 23? c. What sum is most likely to appear? 11. From a group consisting of Alvin, Bob, Carol, and Donna, two people are to be randomly selected to serve on a committee. a. Find the probability that Bob and Carol are selected. b. Find the probability that Carol is not selected. 12. From a standard deck of cards, two cards are randomly drawn, one after the other without replacement. The color of each card is noted. Which is less likely to occur: two red cards or a red card and a black card? Explain. Pre-Calculus Section 4.4 Probability with Combinations 1. Five cards are dealt from a well-shuffled standard deck. a. Using combinations, write an expression for the probability all are hearts. b. Using combinations, write an expression for the probability there are no hearts. c. Using combinations, write an expression for the probability there is at least one heart. 2. Thirteen cards are dealt from a well-shuffled standard deck. a. Using combinations, write an expression for the probability all are clubs. b. Using combinations, write an expression for the probability none are clubs. c. Using combinations, write an expression for the probability there is at least one club. 3. A bag contains five red marbles and three white marbles. If two marbles are randomly drawn, one after the other and without replacement, what is the probability that there is one red marble? 4. A bag contains six red marbles and two white marbles. If two marbles are randomly drawn, one after the other and without replacement, what is the probability that there is one red marble? 5. Free concert tickets are distributed to four students chosen at random from eight juniors and twelve seniors in the school orchestra. What is the probability that free tickets are received by: a. four seniors? b. exactly three seniors? c. exactly two seniors? d. exactly one senior? e. no seniors? 6. A town council consists of eight Democrats, seven Republicans, and five Independents. A committee of three is chosen by randomly pulling names from a hat. a. What is the probability that the committee has two Democrats and one Republican? b. What is the probability that the committee has three Independents? c. What is the probability that the committee has no Independents? d. What is the probability that the committee has one Democrat, one Republican, and one Independent?
5 7. A committee of three people is to be randomly selected from the six people: Archibald, Beatrix, Charlene, Denise, Eloise, and Fernando. a. Find the probability that Eloise is on the committee. b. Find the probability that Eloise and Fernando are on the committee. c. Find the probability that either Eloise or Fernando is on the committee. d. Find the probability that neither Eloise nor Fernando is on the committee. e. Find the probability that Archibald is on the committee and Beatrix is not. f. Find the probability that Denise is on the committee given that Archibald is. g. Find the probability that Denise is on the committee given that neither Archibald nor Beatrix is. 8. Thirteen cards are dealt from a well-shuffled standard deck. a. Using combinations, write an expression for the probability of getting all red cards. b. Using combinations, write an expression for the probability of getting seven diamonds and six hearts. c. Using combinations, write an expression for the probability of getting at least one face card. d. Using combinations, write an expression for the probability of getting all face cards. e. Using combinations, write an expression for the probability of getting all cards form the same suit. f. Using combinations, write an expression for the probability of getting seven spades, three hearts, and three clubs. g. Using combinations, write an expression for the probability of getting all of twelve face cards. h. Using combinations, write an expression for the probability of getting at least one diamond. 9. A committee of four is chosen at random from a group of five married couples. What is the probability that the committee includes no two people who are married to each other? 10. The letters of the word ABRACADABRA are written on separate slips of paper and place din a hat. Five slips of paper are then randomly drawn, one after the other and without replacement. a. What is the probability of getting all A s? b. What is the probability of getting both R s? c. What is the probability of getting at least one B? d. What is the probability of getting at least one of each letter? 11. A quality control inspector randomly inspects four microchips in every lot of 100. If one or more microchips are defective, the entire lot is rejected for shipment. Suppose a lot contains 10 defective microchips and 90 acceptable ones. What is the probability that the lot is rejected? Round your answer to three decimal places. 12. A lot of 20 television sets consists of six defective sets and fourteen good ones. If a sample of three sets is chosen, a. What is the probability the sample contains all defective sets? b. What is the probability that the sample contains at least one defective set? Pre-Calculus Unit 4 Review 1. On a bookshelf there are 10 different algebra books, six different geometry books, and four different calculus books. In how many ways can you choose three books, one of each kind? 2. A standard bridge deck of cards consists of four suits of thirteen cards each. How many five card hands can be dealt that includes four cards from the same suit and one card from a different suit? 3. In how many different ways can a 10-question true-false test be answered if each question much be answered? 4. At Hamburger Heaven, you can order hamburgers with cheese, onion, pickle, relish, mustard, lettuce and/or tomato. How many different combinations of the extras can you order, choosing any three of them? 5. How many ways are there of selecting three cards, with replacement, from a deck of 26 cards? 6. Students are required to answer any eight out of ten questions on a certain test. How many different combinations of eight questions can a student choose to answer? 7. A student council has six seniors, five juniors, and one sophomore as members. In how many ways can a three member council committee be formed that includes one member of each class? 8. How many license plates of five symbols can be made using a letter for the first symbol and digits for the remaining four symbols?
6 9. How many three letter subsets can be formed from the set {P, Q, R, S}? 10. From a group of three men and seven women, how many committees of two men and two women can be formed? 11. There are five persons who are applicants for three different positions in a store, each person being qualified for each position. In how many ways is it possible to fill the positions, if each person can only fill one position? 12. A bag contains four red and six white marbles. How many ways can five marbles be selected if exactly two must be red? 13. The letters r, s, t, u, and v are to be used to form five-letter patterns. How many patterns can be formed if a. repetitions are not allowed? b. repetitions are allowed? 14. If a number having six digits is to be built at random by use of the digits 1, 2, 3, 4, 5, 6, 7 without repetition, find the number of ways the number could be: a. odd b. even c. divisible by five d. greater than 500,000 e. either odd or even 15. What is the probability of getting a total of 6 on a roll of a pair of dice? 16. From a bag containing six nickels, ten dimes, and four quarters. Six coins are drawn at random all at once. What is the probability of getting three nickels, two dimes and one quarter? 17. If a basketball player has a free throw average of 0.80, what is the probability that the player will make two freethrows in a row? 18. There are 52 colored balls in a large tumbler: 13 red, 13 blue, 13 yellow, and 13 green. The balls of each color are lettered A through M. Five balls are chosen at random. a. What is the probability of choosing two of the same letter and three other, different letters? b. What is the probability of choosing two of the same letter, two of a second letter, and the fifth of a different letter? 19. A die is rolled twice. What is the probability of rolling a six on the first roll and a two on the second roll? 20. Dave, Tom, Bob, Roger, and Sergio left their hats at the hat-check room in a restaurant. When they asked for their hats they found that their hats had not been marked. Their hats were returned to them at random. What is the probability that they all received the correct hats? 21. What is the probability of drawing a king or a heart from a well-shuffled deck of cards in one draw? 2. A bag contains four red marbles and six green marbles. A marble is drawn and then replaced. A second drawing is made. What is the probability that a green marble is drawn both times? 23. A bag contains four red marbles and six green marbles. Two marbles are drawn together at random. What is the probability that both marbles are green? 24. If a bag contains five red balls and seven black balls, find the probability of drawing a red ball on one random draw. 25. A bag contains five red and six white balls. If we draw four balls together, find the probability that: a. two are red and two are white b. all are of the same color c. at least three are white
7 26. The probability that a certain man will live ten years is ¼, and that his wife will live ten years is 1/5. Find the probability that: a. both will live 10 years b. the man will live and the wife will not live ten years c. both will die before the end of 10 years d. the man will not live and the wife will live ten years. e. At least one of them will live ten years. f. What is the sum of the answers for parts a, b, c, d? Why? 27. If two dice are thrown what is the probability of throwing a total of seven or eleven? 28. If four men and four women are seated in a row, what is the probability the men and women alternate? 29. If a family of four takes seats at random in a row, what is the probability the father and mother a. sit together? b. Sit on the ends? 30. From five men and seven women, a committee of four is to be chosen by lot. Find the probability that the committee will involve a. four men b. two men and two women c. all men or all women d. at least three women
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
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
More 9.-9.3 Practice Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. ) In how many ways can you answer the questions on
More informationExam 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
More informationProbability 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
More information6) 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
More informationName: Class: Date: ID: A
Class: Date: Chapter 0 review. A lunch menu consists of different kinds of sandwiches, different kinds of soup, and 6 different drinks. How many choices are there for ordering a sandwich, a bowl of soup,
More informationProbability 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
More informationATHS FC Math Department Al Ain Remedial worksheet. Lesson 10.4 (Ellipses)
ATHS FC Math Department Al Ain Remedial worksheet Section Name ID Date Lesson Marks Lesson 10.4 (Ellipses) 10.4, 10.5, 0.4, 0.5 and 0.6 Intervention Plan Page 1 of 19 Gr 12 core c 2 = a 2 b 2 Question
More informationMost 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:
More informationFinite Mathematics MAT 141: Chapter 8 Notes
Finite Mathematics MAT 4: Chapter 8 Notes Counting Principles; More David J. Gisch The Multiplication Principle; Permutations Multiplication Principle Multiplication Principle You can think of the multiplication
More informationUnit 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
More information4.1 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
More informationWeek 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
More informationSimple Counting Problems
Appendix F Counting Principles F1 Appendix F Counting Principles What You Should Learn 1 Count the number of ways an event can occur. 2 Determine the number of ways two or three events can occur using
More informationConditional 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
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Mathematical Ideas Chapter 2 Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) In one town, 2% of all voters are Democrats. If two voters
More informationConditional 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.
More informationChapter 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
More informationName: Spring P. Walston/A. Moore. Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams FCP
Name: Spring 2016 P. Walston/A. Moore Topic worksheet # assigned #completed Teacher s Signature Tree Diagrams 1-0 13 FCP 1-1 16 Combinations/ Permutations Factorials 1-2 22 1-3 20 Intro to Probability
More informationMULTIPLE 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
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Statistics Homework Ch 5 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 information5.8 Problems (last update 30 May 2018)
5.8 Problems (last update 30 May 2018) 1.The lineup or batting order for a baseball team is a list of the nine players on the team indicating the order in which they will bat during the game. a) How many
More informationChapter-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
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 00 -- PRACTICE EXAM 3 Millersville University, Fall 008 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given question,
More informationUnit 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,
More informationUse 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
More information50 Counting Questions
50 Counting Questions Prob-Stats (Math 3350) Fall 2012 Formulas and Notation Permutations: P (n, k) = n!, the number of ordered ways to permute n objects into (n k)! k bins. Combinations: ( ) n k = n!,
More informationInstructions: 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
More informationSection The Multiplication Principle and Permutations
Section 2.1 - The Multiplication Principle and Permutations Example 1: A yogurt shop has 4 flavors (chocolate, vanilla, strawberry, and blueberry) and three sizes (small, medium, and large). How many different
More informationMath 1101 Combinations Handout #17
Math 1101 Combinations Handout #17 1. Compute the following: (a) C(8, 4) (b) C(17, 3) (c) C(20, 5) 2. In the lottery game Megabucks, it used to be that a person chose 6 out of 36 numbers. The order of
More information1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building?
1. An office building contains 27 floors and has 37 offices on each floor. How many offices are in the building? 2. A particular brand of shirt comes in 12 colors, has a male version and a female version,
More informationIntroduction. Firstly however we must look at the Fundamental Principle of Counting (sometimes referred to as the multiplication rule) which states:
Worksheet 4.11 Counting Section 1 Introduction When looking at situations involving counting it is often not practical to count things individually. Instead techniques have been developed to help us count
More information3 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,
More informationAlgebra II- Chapter 12- Test Review
Sections: Counting Principle Permutations Combinations Probability Name Choose the letter of the term that best matches each statement or phrase. 1. An illustration used to show the total number of A.
More information7.1 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
More informationFind 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
More informationTEST 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
More informationSTATISTICAL COUNTING TECHNIQUES
STATISTICAL COUNTING TECHNIQUES I. Counting Principle The counting principle states that if there are n 1 ways of performing the first experiment, n 2 ways of performing the second experiment, n 3 ways
More informationMEP Practice Book SA5
5 Probability 5.1 Probabilities MEP Practice Book SA5 1. Describe the probability of the following events happening, using the terms Certain Very likely Possible Very unlikely Impossible (d) (e) (f) (g)
More informationAlgebra 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)
More informationChapter 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
More informationMEP Practice Book ES5. 1. A coin is tossed, and a die is thrown. List all the possible outcomes.
5 Probability MEP Practice Book ES5 5. Outcome of Two Events 1. A coin is tossed, and a die is thrown. List all the possible outcomes. 2. A die is thrown twice. Copy the diagram below which shows all the
More informationMath 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
More informationCHAPTER 8 Additional Probability Topics
CHAPTER 8 Additional Probability Topics 8.1. Conditional Probability Conditional probability arises in probability experiments when the person performing the experiment is given some extra information
More informationPROBABILITY Case of cards
WORKSHEET NO--1 PROBABILITY Case of cards WORKSHEET NO--2 Case of two die Case of coins WORKSHEET NO--3 1) Fill in the blanks: A. The probability of an impossible event is B. The probability of a sure
More informationChapter 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
More information2. How many different three-member teams can be formed from six students?
KCATM 2011 Probability & Statistics 1. A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the
More informationMATH 215 DISCRETE MATHEMATICS INSTRUCTOR: P. WENG
MATH DISCRETE MATHEMATICS INSTRUCTOR: P. WENG Counting and Probability Suggested Problems Basic Counting Skills, Inclusion-Exclusion, and Complement. (a An office building contains 7 floors and has 7 offices
More informationA. 15 B. 24 C. 45 D. 54
A spinner is divided into 8 equal sections. Lara spins the spinner 120 times. It lands on purple 30 times. How many more times does Lara need to spin the spinner and have it land on purple for the relative
More informationProbability --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..
More informationName: 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
More information1. Simplify 5! 2. Simplify P(4,3) 3. Simplify C(8,5) ? 6. Simplify 5
Algebra 2 Trig H 11.4 and 11.5 Review Complete the following without a calculator: 1. Simplify 5! 2. Simplify P(4,3) 3. Simplify C(8,5) 4. Solve 12C5 12 C 5. Simplify? nc 2? 6. Simplify 5 P 2 7. Simplify
More informationApril 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
More informationChapter 11: Probability and Counting Techniques
Chapter 11: Probability and Counting Techniques Diana Pell Section 11.1: The Fundamental Counting Principle Exercise 1. How many different two-letter words (including nonsense words) can be formed when
More informationSECONDARY 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
More informationSTAT 430/510 Probability Lecture 1: Counting-1
STAT 430/510 Probability Lecture 1: Counting-1 Pengyuan (Penelope) Wang May 22, 2011 Introduction In the early days, probability was associated with games of chance, such as gambling. Probability is describing
More informationUnit 5 Radical Functions & Combinatorics
1 Unit 5 Radical Functions & Combinatorics General Outcome: Develop algebraic and graphical reasoning through the study of relations. Develop algebraic and numeric reasoning that involves combinatorics.
More informationAdvanced 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
More informationThe 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
More information13-6 Probabilities of Mutually Exclusive Events
Determine whether the events are mutually exclusive or not mutually exclusive. Explain your reasoning. 1. drawing a card from a standard deck and getting a jack or a club The jack of clubs is an outcome
More information8.2 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
More informationMath 1070 Sample Exam 1
University of Connecticut Department of Mathematics Math 1070 Sample Exam 1 Exam 1 will cover sections 4.1-4.7 and 5.1-5.4. This sample exam is intended to be used as one of several resources to help you
More informationCHAPTER 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:
More informationContemporary Mathematics Math 1030 Sample Exam I Chapters Time Limit: 90 Minutes No Scratch Paper Calculator Allowed: Scientific
Contemporary Mathematics Math 1030 Sample Exam I Chapters 13-15 Time Limit: 90 Minutes No Scratch Paper Calculator Allowed: Scientific Name: The point value of each problem is in the left-hand margin.
More informationProbability Warm-Up 2
Probability Warm-Up 2 Directions Solve to the best of your ability. (1) Write out the sample space (all possible outcomes) for the following situation: A dice is rolled and then a color is chosen, blue
More informationLEVEL I. 3. In how many ways 4 identical white balls and 6 identical black balls be arranged in a row so that no two white balls are together?
LEVEL I 1. Three numbers are chosen from 1,, 3..., n. In how many ways can the numbers be chosen such that either maximum of these numbers is s or minimum of these numbers is r (r < s)?. Six candidates
More informationChapter 16. Probability. For important terms and definitions refer NCERT text book. (6) NCERT text book page 386 question no.
Chapter 16 Probability For important terms and definitions refer NCERT text book. Type- I Concept : sample space (1)NCERT text book page 386 question no. 1 (*) (2) NCERT text book page 386 question no.
More informationIntermediate 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.
More informationUnit 5, Activity 1, The Counting Principle
Unit 5, Activity 1, The Counting Principle Directions: With a partner find the answer to the following problems. 1. A person buys 3 different shirts (Green, Blue, and Red) and two different pants (Khaki
More information3 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
More informationMathematics 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
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
6. Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the probability. ) A bag contains red marbles, blue marbles, and 8
More informationC) 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
More information2. Let E and F be two events of the same sample space. If P (E) =.55, P (F ) =.70, and
c Dr. Patrice Poage, August 23, 2017 1 1324 Exam 1 Review NOTE: This review in and of itself does NOT prepare you for the test. You should be doing this review in addition to all your suggested homework,
More informationFundamental Counting Principle
Lesson 88 Probability with Combinatorics HL2 Math - Santowski Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when there are two or more
More informationSection 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
More informationUniversity of Connecticut Department of Mathematics
University of Connecticut Department of Mathematics Math 070Q Exam A Fall 07 Name: TA Name: Discussion: Read This First! This is a closed notes, closed book exam. You cannot receive aid on this exam from
More informationAlg 2/Trig Honors Qtr 3 Review
Alg 2/Trig Honors Qtr 3 Review Chapter 5 Exponents and Logs 1) Graph: a. y 3x b. y log3 x c. y log2(x 2) d. y 2x 1 3 2) Solve each equation. Find a common base!! a) 52n 1 625 b) 42x 8x 1 c) 27x 9x 6 3)
More informationHere 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.)
More informationProbability Study Guide Date Block
Probability Study Guide Name Date Block In a regular deck of 52 cards, face cards are Kings, Queens, and Jacks. Find the following probabilities, if one card is drawn: 1)P(not King) 2) P(black and King)
More informationProbability Review 41
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.
More informationProbability Review Questions
Probability Review Questions Short Answer 1. State whether the following events are mutually exclusive and explain your reasoning. Selecting a prime number or selecting an even number from a set of 10
More informationExercises Exercises. 1. List all the permutations of {a, b, c}. 2. How many different permutations are there of the set {a, b, c, d, e, f, g}?
Exercises Exercises 1. List all the permutations of {a, b, c}. 2. How many different permutations are there of the set {a, b, c, d, e, f, g}? 3. How many permutations of {a, b, c, d, e, f, g} end with
More informationSection 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
More informationQ1) 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.
More informationMAT 17: Introduction to Mathematics Final Exam Review Packet. B. Use the following definitions to write the indicated set for each exercise below:
MAT 17: Introduction to Mathematics Final Exam Review Packet A. Using set notation, rewrite each set definition below as the specific collection of elements described enclosed in braces. Use the following
More informationProbability, Permutations, & Combinations LESSON 11.1
Probability, Permutations, & Combinations LESSON 11.1 Objective Define probability Use the counting principle Know the difference between combination and permutation Find probability Probability PROBABILITY:
More informationCounting Principles Review
Counting Principles Review 1. A magazine poll sampling 100 people gives that following results: 17 read magazine A 18 read magazine B 14 read magazine C 8 read magazines A and B 7 read magazines A and
More informationAlgebra II Probability and Statistics
Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Slide 3 / 241 Table of Contents click on the topic to go to that section Sets Independence and Conditional Probability
More informationPROBABILITY. 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
More information4.3 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:
More informationUnit 8, Activity 1, Vocabulary Self-Awareness Chart
Unit 8, Activity 1, Vocabulary Self-Awareness Chart Vocabulary Self-Awareness Chart WORD +? EXAMPLE DEFINITION Central Tendency Mean Median Mode Range Quartile Interquartile Range Standard deviation Stem
More informationCounting Methods and Probability
CHAPTER Counting Methods and Probability Many good basketball players can make 90% of their free throws. However, the likelihood of a player making several free throws in a row will be less than 90%. You
More informationout one marble and then a second marble without replacing the first. What is the probability that both marbles will be white?
Example: Leah places four white marbles and two black marbles in a bag She plans to draw out one marble and then a second marble without replacing the first What is the probability that both marbles will
More informationAlgebra II. Slide 1 / 241. Slide 2 / 241. Slide 3 / 241. Probability and Statistics. Table of Contents click on the topic to go to that section
Slide 1 / 241 Slide 2 / 241 Algebra II Probability and Statistics 2016-01-15 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 241 Sets Independence and Conditional Probability
More informationDirections: Solve the following problems. Circle your answers. length = 7 cm. width = 4 cm. height = 3 cm
length = 7 cm width = 4 cm height = 3 cm 2. Heidi has an odd number of stamps in her collection. The sum of the digits in the number of stamps she has is 12. The hundreds digit is three times the ones
More informationMath 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,
More informationMath 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,
More informationChapter 1 - Set Theory
Midterm review Math 3201 Name: Chapter 1 - Set Theory Part 1: Multiple Choice : 1) U = {hockey, basketball, golf, tennis, volleyball, soccer}. If B = {sports that use a ball}, which element would be in
More informationCounting (Enumerative Combinatorics) X. Zhang, Fordham Univ.
Counting (Enumerative Combinatorics) X. Zhang, Fordham Univ. 1 Chance of winning?! What s the chances of winning New York Megamillion Jackpot!! just pick 5 numbers from 1 to 56, plus a mega ball number
More information