Math 141 WIR, Spring 2007,cBenjamin AurispaMath 141 Exam 2 Review Problem SetNote: Not every topic is covered in this review. It is more heavily weighted on Sections 6.4 &7.1-7.3, since these are new. Please also take a look at the previous Week in Reviews for morepractice problems on other sections.1. An experiment consists of observing the outcomes when you toss a coin and then randomlyselect a marble from a jar filled with 3 red, 2 blue, and 5 green marbles.(a) What is the sample space for this experiment?(b) Describe the event E that a red marble is drawn.(c) Describe the event F that a tail is tossed or a green marble is drawn.(d) Are E and F mutually exclusive events?(e) Is this a uniform sample space? Why or why not?2. A pair of fair dice is rolled. We know the sample space for this experiment is:S =(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)(a) Is this a uniform sample space? Why or why not?(b) Calculate the probability that the product of the two numbers rolled is 6 or 8.(c) Calculate the probability that the product of the numbers is 4 or the sum of the numbersis 4.3. A bag of Skittles contains 13 yellow, 11 green, 9 orange, 6 red, and 5 purple. I reach in andpull out one Skittle.(a) What is the probability distribution for this experiment?(b) Calculate the probability that I will get a green or an orange.(c) Calculate the probability that I will not get a purple.4. Suppose P (E) = .4, P (F ) = .5, and P (E ∪ F ) = .6. Calculate the following.(a) P (E ∩ F )(b) P (Fc)(c) P (Ec∪ Fc)(d) P (Ec∩ F )5. 500 people were surveyed about what Oscar-nominated movies they had seen. 264 of them hadseen The Departed while 175 of them had seen Babel. 150 people had seen neither. What isthe probability that a person selected at random from this group1Math 141 WIR, Spring 2007,cBenjamin Aurispa(a) Had seen both?(b) Had seen The Departed but not Babel?(c) Had seen at least one of these two movies?(d) Had not seen Babel ?6. In the game of Rummikub, there are 52 tiles. The tiles are divided into four colored sets,each consisting of the numbers 1 through 13. The four colors are blue, black, red, and orange.Suppose that all the tiles are put into a bag and one tile is selected at random. Calculate theprobability that(a) A red or black tile is selected.(b) A blue tile is not selected.(c) An orange tile or a 9 is selected.(d) Neither a black tile nor a 12 is selected. (A black tile or a 12 is NOT selected.)7. A chef has 20 different recipes that she wants to arrange in her recipe book. She has 9 dessertrecipes, 6 entree recipes, and 5 appetizer recipes.(a) How many ways are there to arrange all 20 recipes in the book?(b) How many ways are there to arrange the recipes if she wants all the dessert recipestogether, all the entree recipes together, and all the appetizer recipes together?8. In a graduating class of 200 students, there will be one valedictorian, one salutatorian, and agroup of 18 others will be in the top ten percent of the class. In how many different ways couldthe school have a valedictorian, salutatorian, and the rest of the top ten percent (assuming weknow nothing about grades.)9. A bag of marbles consists of 7 red, 9 green, and 10 yellow. Suppose a sample of 6 marbles isselected.(a) How many samples would contain exactly 4 reds?(b) How many samples would contain at least 3 green?(c) How many samples would contain no green marbles?(d) How many samples would contain exactly 3 yellow or exactly 2 red?10. A grocery store stocker needs to stock a shelf with 7 identical cans of soup, 6 identical boxesof cereal, and 5 identical bottles of ketchup. He is in Math 141, so he starts rearranging all theitems in a row in different ways. How many DIFFERENT arrangements are possible?11. Let U = {a, b, c, d, e, f, g, h, i, j}, A = {a, d, h, j}, B = {b, e, f, i}, C = {e, h}, and D = {a, j}.Determine whether the following statements are True or False.(a) TRUE FALSE D ⊆ A(b) TRUE FALSE C ⊂ B(c) TRUE FALSE g ∈ A ∪ B(d) TRUE FALSE (A ∩ B)c= U2Math 141 WIR, Spring 2007,cBenjamin Aurispa(e) TRUE FALSE (B ∩ C) ∪ D = ∅(f) TRUE FALSE n((A ∪ B)c) = 2(g) TRUE FALSE n((D ∪ C) ∩ A) = 4(h) TRUE FALSE C and D are disjoint sets.12. A certain high school offers 3 AP exams: Calculus, U.S. History, and English. There are 185students in the senior class. Data is given below of how many seniors took these AP exams.17 seniors took English and History, but not Calculus.30 seniors took only Calculus.41 seniors took Calculus and History.43 seniors took exactly 2 AP exams.127 seniors took Calculus or English.84 seniors took History.25 seniors took all three AP exams.(a) How many seniors did not take any of these AP exams?(b) How many seniors took exactly 1 AP exam?(c) How many seniors took Calculus or English, but not History?13. How many 5-digit numbers are possible if the 1st, 3rd, and 5th digits must be odd, the 2ndand 4th digits must be even, and there can be no repetitions.14. Minimize C = 2x + 4ySubject to:x + y ≤ 10x + 2y ≥ 14x ≥ 2y ≥ 015. A local business makes peanut butter and jelly sandwiches in two sizes, small and large. Eachsmall sandwich makes a profit of $2 and uses 3 ounces of peanut butter and 4 ounces of jelly.Each large sandwich makes a profit of $5 and uses 5 ounces of peanut butter and 5 ounces ofjelly. The business only has 30 ounces of peanut butter and 35 ounces of jelly available to useeach hour. How many of each size of sandwich should be sold each hour in order to maximizeprofit? Are there any leftovers?16. A sporting event sells tickets for children, students, and adults. A child ticket sells for $10, astudent ticket sells for $20, and an adult ticket sells for $25. The arena in which the sportingevent is held holds 15000 people. The management wants to sell at least 4 times as many adulttickets as child tickets. Also, the money made from student tickets should be at most one-thirdof the money made from adult tickets. The last stipulation is that the number of adult ticketssold should be at least half the total number of tickets sold. How many child, student, andadult tickets should be sold in order
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