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210HWChapter05 - a Experiment = play the game or test the...

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Unformatted text preview: a) Experiment = play the game or test the game b) 75 of the veteran game players said that it had bad playability 65 is not a probability because the number 65 is not between 0 c) and 1, inclusive. d) The number -1 is not between the numbers 0 and 1, inclusive. e) After the tests were all done, 54 said they did not like it count said liked it empirical or relative frequency 80 65 0.8125 1 a) Total cards # of queens in 1 deck Probability of selecting a Queen 52 4 0.0769230769 Classical because there are n equally likely outcomes b) 2 a) Total Children Marital Status of Parents Divorced Married 539 333 P(Married) = P(Divorced) = 0.6178107607 Widowed 182 24 P(Widowed) = 0.3376623377 0.0445269017 Empirical Probability or Relative Frequency because the problem uses past date to calculate a probability that could be used for future estimation. Law of Large Numbers says that as the number of b) Trials the Relative Frequency will approach the true probability. 3 a) 1 because it is above 12,000. The book was written a while ago. I guess it could be either classical or empirical because 1/1 = 1 ==> 100%. You could say its likelihood is 1, but in some ways it could be argued that it is none of the b) approaches to probability because it is one, known event from the past. Equal? TRUE Two People = Favor = F Against = A Possible Outcomes Outcome 1 F, F Outcome 2 F, A Outcome 3 A, A Outcome 4 A, F 2 Majors Acc Fin Econ Manage Market Total a) 34 Prob Name Probability Number P(Acc) = 0.2941176471 P(Fin) = 0.1470588235 P(Econ) = 0.0882352941 P(Manage) 0.1764705882 = P(Market) = 0.2941176471 Total b) # of Students Declaring Major 10 5 3 6 10 1 This is the Relative Frequency or Empirical Approach Total Candidates Minority a) b) P(Minority) = Classical because there are n equally likely outcomes 5 2 0.4 a) b) c) d) Relative Frequency or Empirical Classical Classical, but still extremely remote chance of winning Empirical based on past data. Sample size = People asked Yes or No question: 40 Oil Executives The experiment was the asking the 40 executives a) the Yes/No environmental question b) All 40 said No. c) Answered Yes P(Yes) = 10 d) Relative Frequency or Empirical e) No, not both. Each of the possible outcomes are not equally likely. For example ==> 0.25 1 possible outcome is this many said yes: 2 possible outcome is this many said yes: 12 P(Yes) = 0.3 The possible outcomes are mutually exclusive because you can't have the group have 12 say yes and 19 say yes also. 19 P(Yes) = 0.475 Number of Violations Number of Drivers 0 1,910 1 46 2 18 3 12 4 9 5 or more 5 Total 2,000 The experiment is seeing how many speeding violations people have from a sample of 2000 people. One possible event is 1 speeding violation. Another example of b) one possible event is one or more violations. c) 0.009 d) Empirical or Relative Frequency a) Table of possible probabilities P(exactly 0 speeding violations) = P(exactly 1 speeding violations) = P(exactly 2 speeding violations) = P(exactly 3 speeding violations) = P(exactly 4 speeding violations) = P(5 or more speeding violations) = P(3 or more) = 0.006 + 0.0045 + 0.0025 = 0.955 0.023 0.009 0.006 0.0045 0.0025 0.013 c7466754d66532ff4fbbea246d745bff7605e657.xls - SR 5-3 Classifications Event Supervisors A Maintenance B Production C Management D Secretarial E # of Employees 120 50 1460 302 68 2000 P(X) P(A) P(B) P(C) P(D) P(E) P(X) 0.06 0.025 0.73 0.151 0.034 1 a) i P(Maintenance or Secretarial) ii P(Not Management) = P(B or E) = = P(Not D) = b) Management Maintenance Secretarial c) (a)(i) P(B) P(E) Total Mutually Exclusive and not complimentary (not complimentary because they don't add up to 1) 0.025 0.034 0.059 0.025 + 1- 0.034 = 0.151 = 0.059 0.849 Need corrective shoes Need major dental work Percent that need corrective shoes and major dental work BOTH a) P(Need corrective shoes OR Need major dental work) = 0.15 + 0.08 - 0.03 = 8.00% 15.00% 3.00% Must subtract so you don't double count the 3.00% is BOTH 20.00% b) Need corrective shoes Need major dental work c7466754d66532ff4fbbea246d745bff7605e657.xls - Ex13 Income After Taxes Number of Firms Event Under $1 million 102 A $1 million to $20 million 61 B $20 million or more 37 C 200 P(X) P(A) P(B) P(C) P(X) 0.51 0.305 0.185 1 a) P(A) 0.51 P($1 million to $20 million or $20 million or b) more) = 0.3050 + 0.1850 0.0000 = 0.4900 Special Rule because the categories are mutually exclusive. However, if you used the General Rule, the joint probability would have been zero and you would have gotten the correct answer. Profit Break Even Lose Total a) b) P(Profit OR Break Even) = 0.5 + 0.3 = P(Profit OR Break Even) = 1 - 0.2 = 50% 30% 20% 100% 80% 80% A B 0.25 0.5 P( above C) =0.25 + 0.5 = 0.75 Two Coins are tossed A= B= H,H T,T P(H,H) = P(T,T) = Total 0.25 0.25 0.5 The two are mutually exclusive because the two events cannot happen at the same time. Two events, A & B, are mutually exclusive if both events, A & B, cannot occur at the same time a) b) No, because they do not add up to 1, they add up to .5 All Possible Outcomes 1 H,H 2 H,T 3 T,T 4 T,H Total 4 0.25 0.25 0.25 0.25 1 Events A B A AND B P(A OR B) = 0.2 + 0.3 - 0.15 = P(X) P(X) P(A) = 0.2 P(B) = 0.3 P(A AND B) = 0.15 0.35 P F D P&F&D P&D F&D P&F a) b) c) d) Southwest Grocery Stores Had Pharmacy Had Floral Shop Had Deli Had All 3 Had Pharmacy and Deli Had Floral Shop and Deli Had Pharmacy and Floral P(Had Pharmacy and Had Floral Shop) = P(Had Pharmacy and Had Deli) = No. Because, for example, if you select a store with a deli, it could be in a category "Deli only" or "Deli and Pharmacy". Joint Probability 0.4 0.5 0.7 0.1 0.3 0.25 0.2 P(F) = 0.5 0.2 0.3 P(D) = 0.7 e) Step 1: Find P(P or F or D) Step 2: Find 1 - P(P or F or D) = Notes: This is to add the Probability This is to not double count This if for the triple count Once you have all that you can subtract it from 1 P(P) = 0.4 P(P OR F OR D) = P(P) + P(F) + P(D) - P(P & D) P(F & D) - P(P & F) + P(P & F & D) 0.05 0.95 =C2+C3+C4-C6-C7-C8+C5 P(P) + P(F) + P(D) - P(P & D) - P(F & D) - P(P & F) + P(P & F & D) 1 - 0.95 = 0.05 P(P) = 0.4 P(F) = 0.5 P(D) = 0.7 This problem was not assigned Vacationers Going To Rocky Mountain Region Yellowstone 0.5 Tetons 0.4 Yellowstone and Tetons 0.35 P(Y) = P(T) = P(Y and T) = 0.5 + 0.4 - 0.35 = P(Y and T) = 0.5 + 0.4 - 0.35 = 0.35 0.50 0.40 0.55 a) P(Y and T) = 0.5 + 0.4 - 0.35 = 0.55 Notes: P("visit at least one" means Y or T or Both) But you can't double count b) "Joint" or "Concurrent" No because of the overlapping circles c) in the Venn Diagram to the right ==> P(Y) = Vacationers destinations according to National Park Service P(X) Compliment Yellowstone 0.5 0.5 Tetons 0.4 0.6 Yellowstone and Tetons 0.35 Visit only Yellowstone (0.5*(1-0.4)) Visit only Tetons (0.4*(1-0.5)) Yellowstone and Tetons 0.3 0.2 0.35 Done with formulas that take more time than they are worth P(Y) = P(T) = P(Y and T) = 0.50 0.40 0.55 P(T) = P(Y and T) = 0.5 + 0.4 - 0.35 = 0.35 a) 4/52 = 2/26 = 1/13 ==> because the sample space has not changed b) 3/51 because there are only 3 kings and the sample space has changed c) P(2 straight Kings) = 4/52*3/51 = 0.0045249 4 52 3 51 a) b) c) d) Derreck Lee Highest Ave in 2005 Season 0.335 Assume he hits in one game = 3 Empirical because it is based on past data and we are using it to estimate how he will do for the game P(3 straight hits ) = 0.335*0.335*0.335 = 0.037595375 0.0375954 P(No Hits) = (1-0.335)*(1-0.335)*(1-0.335) = (1-0.335)^3 = 0.294079625 0.2940796 P(at least 1 hit) = P(1 or 2 or 3 hits) = 1 - P(No Hits) = 0.7059204 or d) P(1) = P(1 hit, No hit, No Hit) + P(No hit, 1 Hit, No Hit) + P(No hit, No Hit, 1 hit) = P(2) = P(1 hit, 1 hit, No Hit) + P(1 Hit, No Hit, 1 hit) + P(No hit, 1 hit, 1 hit) = P(3) = P(1 hit, 1 hit, 1hit) = P(at least 1 hit) = P(1 or 2 or 3 hits) = 0.4444361 0.2238889 0.0375954 0.7059204 H NH DL Average = Probability of getting a hit DL Average = Probability of NOT getting a hit # of at bats = # of Trials = Because averages do not include walks, hit by pitch, sacrifices, and other non-Hits/NotHits in the calculation, The events H and NH are mutually exclusive and independent and the categories H and NH are collectively exhaustive. a b c d Empirical P(H and H and H) = P(H)*P(H)*P(H) = P(0) P(at least one hit) = P(1 or 2 or 3) 0.335 P(H) 0.665 P(NH) 3 0.037595375 0.294079625 0.705920375 check check 0.0376 0.0376 0.29408 0.70592 # of Possible outcomes in the sample space = ss = Possible Outcomes # of at bats = # of Trials = 1 2 1H H H 2H H NH 3H NH H 4 NH H H 5H NH NH 6 NH H NH 7 NH NH H 8 NH NH NH 8 3 # of Hits Probability out of 3 at of bats Occurance 3 2 2 2 1 1 1 0 0.03759538 0.07462963 0.07462963 0.07462963 0.14814538 0.14814538 0.14814538 0.29407963 1 Random Variable = X = # of Hits in 3 at bats P(X) 0 P(0) 1 P(1) 2 P(2) 3 P(3) P(X) 0.2940796 0.4444361 0.2238889 0.0375954 1 Teton Tires Failure hurdle P(XB-70 tire will last 60,000 before it becomes bald or fail) An adjustment is made on any tire that does not last 60,000 We purchase this # of tires: P(All 4 tires will last 60,000 miles) = 0.8*0.8*0.8*0.8 = 0.8^4 = 60,000 0.8 4 0.4096 Board of Directors Men Women Total Wee need to select a committee with 4 members at random 8 4 12 4 Sample Space Conditional Women Selected Changes Probability 4 12 0.3333333333 3 11 0.2727272727 2 10 0.2 1 9 0.1111111111 a) b) c) P(All Women) = 8/12*7/11*6/10*5/9 = 0.141414141414141 = P(All Men) = 4/12*3/11*2/10*1/9 = 0.00202020202020202 = No because 0.141414141414141 + 0.00202020202020202 Does not equal 1. In addition, there are other possibilities such as, for example, 3 women and a man. Also, the categories are not collectively exhaustive. Men Selected Sample Space Conditional Changes Probability 8 12 0.6666666667 7 11 0.6363636364 6 10 0.6 5 9 0.5555555556 0.1414141414 0.0020202020 Executives were asked whether or not they would remain with the company if they received a better offer from a different company Length of Service Less than 1-5 More than Loyalty 1 year years 6-10 years 10 years Total Would remain 10 30 5 75 120 Would not remain 25 15 10 30 80 35 45 15 105 200 P(Randomly selecting executive who has More than 10 years) = a) 105/200 = P(Randomly selecting executive who Would not remain GIVEN b) THAT More than 10 years) = 30/105 = P(Randomly selecting executive who has More than 10 years OR c) Would not remain) = 105/200 + 80/200 - 30/200 = P(Randomly selecting executive who Would remain AND who has More than 10 years) = P(Randomly selecting executive who Would not remain AND who has More than 10 years) = 0.525000 0.285714 0.775 0.375 0.375 0.15 0.15 Visits Yes Often Occasional Never Total a) b) Visits Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Often Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Occasional Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Never Enclosed Mall No Total 60 20 80 25 35 60 5 50 55 90 105 195 Because Independence means that the occurrence of one event does not affect the occurrence of another event, for our two variables "Visits" and "Enclosed Mall", they are not independent. Using the Rule of Independence, we can show that P(Never|Yes) Does Not Equal P(Never) ==> 5/90 Does Not Equal 55/195 Enclosed Mall Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No No No No No No No No No No No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No Yes Yes Yes Yes Yes No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No No Enclosed Mall Visits Often Occasional Never Grand Total Data Yes CondProb Count of Visits 2/ 3 5/ 18 1/ 18 1/ 1 4/ 13 5/ 39 1/ 39 6/ 13 JointProb 30.77% 12.82% 2.56% 46.15% Count of Visits 60 25 5 90/ 1 Data Yes CondProb 66.67% 27.78% 5.56% 100.00% Data Yes CondProb 0.6666666667 0.2777777778 0.0555555556 1 JointProb 0.3076923077 0.1282051282 0.0256410256 0.4615384615 Count of Visits Count of Visits Enclosed Mall Visits Often Occasional Never Grand Total No CondProb Count of Visits 60 25 5 90 Enclosed Mall Visits Often Occasional Never Grand Total JointProb Count of Visits 60 25 5 90 JointProb 20 35 50 105 4/ 21 1/ 3 10/ 21 1/ 1 4/ 39 7/ 39 10/ 39 7/ 13 20 35 50 105/ 1 No CondProb 19.05% 33.33% 47.62% 100.00% JointProb 10.26% 17.95% 25.64% 53.85% No CondProb 0.1904761905 0.3333333333 0.4761904762 1 JointProb 0.1025641026 0.1794871795 0.2564102564 0.5384615385 20 35 50 105 done with PivotTable and Fractional Number Format Done with formulas and % format Done with PivotTable and Custom Fraction Number Format 25 a) b) P(Checking) P(Savings) P(C & S) P(C OR S) = 0.8 + 0.6 - 0.5 = P(Not C OR S) = 1 - +0.9 = 0.8 0.6 0.5 0.9 0.1 26 P(1st truck available) = P(2nd truck available) = P(Both 1st and 2nd truck available) = Step 1: Find P(1st OR 2nd) = 0.75 + 0.5 - 0.3 = Step 2: Find P(neither available) = 1 - P(1st OR 2nd) = 1 - 0.95 = 0.75 0.5 0.3 Remember: P(1st OR 2nd) means 1st is working, or second is 0.95 working or Both are working. 0.05 So that means that 1 - P(1st OR 2nd) means neither are working Defective Toothbrushes = Non-Defective Toothbrushes = Total a) b) P(first 2 brushes are not defective) =3/20*2/19 = 0.0157894736842105 P(first 2 brushes are not defective) =17/20*16/19 = 0.715789473684211 3 17 20 0.0157894737 Sample Space Changes 0.7157894737 Sample Space Changes c7466754d66532ff4fbbea246d745bff7605e657.xls - Ex29 Potential for advancement Fair Sales Ability Below Ave. Ave. Above Ave. Totals Good 16 45 93 154 Excellent Totals 12 60 72 144 22 50 45 150 135 300 202 500 Sales Ability Fair Below Ave. Ave. Above Ave. Joint Probabilities Good 0.032 0.09 0.186 Excellent 0.024 0.12 0.144 0.044 0.09 0.27 SUM = a) b) c) Contingency Table: Good for Nominal Data P(Above Ave. Sales Ability AND Excellent Potential for advancement) = 135/500 = 0.27 0.27 1 c7466754d66532ff4fbbea246d745bff7605e657.xls - Ex29 (2) Potential for advancement Good Sales Ability 16 45 93 154 Excellent 12 60 72 144 Totals 22 50 45 150 135 300 202 500 Sales Ability Below Ave. Ave. Above Ave. Fair Joint Probabilities Good 3.20% 9.00% 18.60% Excellent 2.40% 12.00% 14.40% 4.40% 9.00% 27.00% SUM = Contingency Table: Good for Nominal Data P(Above Ave. Sales Ability AND Excellent Potential for advancement) = 135/500 = a) b) c) PotForAd Sales Ability Below Ave. Ave. Above Ave. Grand Total Count 16 45 93 154 0.27 0.27 Data Fair CondProb 32.00% 30.00% 31.00% 30.80% JointProb 3.20% 9.00% 18.60% 30.80% Count 12 60 72 144 Good CondProb 24.00% 40.00% 24.00% 28.80% JointProb 2.40% 12.00% 14.40% 28.80% Count 22 45 135 202 Excellent CondProb 44.00% 30.00% 45.00% 40.40% JointProb 4.40% 9.00% 27.00% 40.40% 100.00% 1 2 3 4 5 6 Sales Ability Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Potential for advancement Fair Fair Fair Fair Fair Fair 7 Fair Below Ave. Ave. Above Ave. Totals Below Ave. Fair 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Below Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Above Ave. Abo...
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