{ 10,12,17} { 4, 7,13}

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1 Math 13 L Shipley Exam #3 Review Spring 2011 Exam #3 will cover chapter 6, and the first two sections of chapter 7. This review will give you an idea about what types of concepts will be covered on the exam. On the day of the exam, you may bring a 5x7 card with helpful formulas written on it and an approved calculator. ll electronic devises, such as cell phones and MP3 players, must be turned off during the exam. egin preparing as soon as possible, and be sure to ask either myself or staff at the MLC for help on any areas that you feel you need explaining. Do your best. Examples of problems from True or false: If = { 9,10,12,14,17} { 10,12,17} 2. True or false: If = { 2, 4, 7,10,13} { 4, 7,13} = = = 3. Consider the sets,, and C given by = { 3,5, 6,8,11}, = { 5, 6,11}, and C = { 3,8} Which of the following statements are true ) ( C) = ) ( ) = C C) ( ) C = C D) ( ) C = { } 4. oston's 5 most frequented restaurants in 2006, according to oston magazine, are listed in the following set: = { Cafe Ronaldo, Venetian, India Cafe, ombay istro, Chef Wong's }, while oston's most admired restaurants are listed in the set = { Cafe Ronaldo, ertucci's, Pizzeria no, ombay istro, Chef Wong's } Find and explain what it means. 5. There were 10 brands of Televisions reviewed by Howie's List. They were LG, JVC, Dynex, Sharp, Panasonic, Philips, Sony, Toshiba, Pioneer, Samsung. What Consumers Digest found was that the 5 most reliable brands were = { LG, JVC, Philips, Pioneer, Samsung }, while the 5 televisions of best value were = { LG, Philips, Sony, Sharp, Panasonic } Find and explain what it means.

2 6. Which of the following Venn diagrams illustrates the set ) ) C) D)

3 7. Which of the following Venn diagrams illustrates the set ) ) C) D) 8. Consider the universal set, and the sets,, and C given by 1, 2,3,5,8,9,10 1,8,9 2,3,8 C = 2,9 = { }, = { } = { }, and { } a) Find a) b) ( ) C c) ( C) d) C e)

4 Examples of problems from Find n( ) given that n( ) = 79, n( ) = 75, and n( ) = Suppose that out of 2000 students at a certain high school, 410 are taking history, 400 are taking chemistry, and 160 are taking both history and chemistry. How many students are taking either history or chemistry 11. Consider the following diagram: C 10 How many elements are in set or set 12. Consider the following diagram: C 10 How many elements are in set or or C

5 13. Suppose 254 CEO's were surveyed about their companies industry type and geographic location in the nited States. Suppose further that the CEO's were allowed to choose only one type of industry (Manufacturing, Communications, and Finance) and one geographic location (Northeast, Southeast, Northwest, Southwest). Northeast Southeast Northwest Southwest Manufacturing Communications Finance Find a) The number of CEO's whose response were not Communications b) The number of CEO's whose responses were Manufacturing or Northwest. c) The number of CEO's whose responses were either Manufacturing or Communications, but not in the Southeast. 14. Find n( ) given that n( ) = 84, n( ) = 66, and n( ) = Suppose that out of 1800 students at a certain college, 360 are taking psychology, 330 are taking biology, and 180 are taking both psychology and biology. How many students are taking either psychology or biology Examples of problems from License plates in Massachusetts consist of three letters followed by three digits. How many different types of plates can be made ) 17,576,010 ) 17,576,050 C) 17,576,000 D) 17,575, License plates in Massachusetts consist of three letters followed by three digits. How many different types of plates can be made if no letter are repeated and no digits are repeated ) 11,232,010 ) 11,232,000 C) 11,231,980 D) 11,232, Suppose you are forming a password. The password will have 8 characters consisting of the 5 digits 0 through 4, and the 5 letters,, C, D, and E. How many different types of passwords can you form if you are not allowed to repeat any character 19. You and a friend are going out to eat. The restaurant has 7 different appetizers, 3 different soups, 12 different entrees, and 8 different desserts. How many different types of meals can you form if you order an appetizer, soup, entree, and dessert

6 Example problems from Evaluate the expression 5! 1!4! Simplify the expression 47! 22. committee is made up of 5 people. If there are 19 people from which to pick the committee, how many different ways are there to make up the committee 23. ll we know about Sarah, Junghan, and Nadya is that they have different birthdays. If we listed all the possible ways this could occur, how many would there be 24. music library is made up of 10 CD's. How many different ways could a person order them on a shelf 25. television network has 4 hour time slots to fill. If there are 10 shows to choose from, how many different lineups are possible 26. Evaluate 10! 27. club is made up of 5 people. If there are 17 people from which to pick the club, how many different ways are there to make up the club Examples of problems from se the formula for C(n,r) to evaluate C(16,12) 29. How many different ways are there to line up 8 people if the order is unimportant 30. There are 11 books on the top shelf of a bookcase. If you choose 3 of them to line up on the second shelf, how many different ways are there to to line them up if order is unimportant 31. Choose 19 letters from the alphabet. without repeating a letter. How many different combinations can you make if the order is unimportant 32. How many eleven-letter words (real or imaginary) can be formed from the letters of the word Mathematics

7 Examples of problems from What is the coefficient of the x 4 6 term in the expansion of ( x 8) What is What is the coefficient of the x 2 y 8 term in the expansion of ( x + y) 36. How many subsets does a set with 5 elements have Examples of problems from Suppose you toss a coin and die. Describe the sample space 38. Suppose you toss a coin. The coin is weighted so that head {H} is 7 times more likely to occur than tails. Construct a probability model for this experiment. 39. Find the number of outcomes of the sample space associated with the experiment of tossing a coin 2 times. 40. Find the number of outcomes of the sample space associated with the experiment of tossing 9 dice. 41. Find the number of outcomes of the sample space associated with the experiment of selecting 3 cards from a regular deck of 52 cards assuming order is not important. 42. Find the number of outcomes of the sample space associated with the experiment of tossing 3 dice and 3 coins. 43. Find the number of outcomes of the sample space associated with the experiment of tossing 4 dice, 2 coins, and picking 2 cards from a regular deck of cards without replacement. 44. Find the number of outcomes of the sample space associated with the experiment of selecting 4 cards from a regular deck of 52 cards assuming order is important. 10

8 45. Suppose 219 CEO's were surveyed about their companies industry type and geographic location in the nited States. Suppose further that the CEO's were allowed to choose only one type of industry (Manufacturing, Communications, Finance) and one geographic location (Northeast, Southeast, Northwest, Southwest). Northeast Southeast Northwest Southwest Manufacturing Communications Finance Find the following probabilities. a) CEO's response was that their companies industry was not Communications b) CEO's response was that their companies industry was Manufacturing or in the Northwest. c) CEO's response was that their companies industry was Manufacturing or Communications but not in the Southeast. Examples of problems from Suppose E and F are mutually exclusive events and P( E ) = 0.22 and P( F ) = 0.17, then what is P( E F) 47. Suppose E and F are mutually exclusive events and P( E ) = 0.2 and P( F ) = 0.22, then what is P( E F) 48. Suppose P( E ) = 0.26, P( F ) = 0.41, and P( E F ) = 0.51 then what is P( E F) 49. Suppose P( E ) = 0.38, P( E F ) = 0.39, and P( E F ) = 0.28 then what is P( F ) 50. Suppose E, F, and G are mutually exclusive events and P( E ) = 0.3, P( F ) = 0.08, and P( F ) = 0.05 then what is P( E F G) 51. Suppose E, F, and G are mutually exclusive events and P( E ) = 0.26, P( F ) = 0.24, and P( F ) = 0.15 then what is P( E F G) 52. group of people are at a conference, and the following table shows the percentages of their hair type. Hair Type Percentage rown 38% lack 7% londe 17% Red 34% ald 4% Find the probability that a) person has brown hair or black hair b) person is bald c) person isn't blonde

9 53. group of people are at a conference, and the following table shows the percentages of their hair type. Hair Type Percentage rown 31% lack 24% londe 8% Red 27% ald 10% Suppose E = {rown, lack} and F = { londe, lack, Red }, what is a) P( E ) b) P( F ) c) P( E F) 54. Suppose the odds for the merican League winning the ll Star game are 9 to 4, what is the probability of the merican League winning the ll Star game 55. Suppose the odds for the merican League winning the ll Star game are 8 to 4, what is the probability of the merican League losing the ll Star game 56. fter a survey of the number of cell phones a household own, the following probability table was constructed. Number of Cell Phones Probability or more 0.09 Find the probability that a) household owns 1 or 2 cell phones b) household owns 3 or fewer cell phones c) household owns 3 or more cell phones

If S = {O 1, O 2,, O n }, where O i is the i th elementary outcome, and p i is the probability of the i th elementary outcome, then

If S = {O 1, O 2,, O n }, where O i is the i th elementary outcome, and p i is the probability of the i th elementary outcome, then 1.1 Probabilities Def n: A random experiment is a process that, when performed, results in one and only one of many observations (or outcomes). The sample space S is the set of all elementary outcomes