141 homework problems, 12B-copyright Joe Kahlig Chapter 8 Solutions, Page 1Chapter 8 Homework SolutionsCompiled by Joe Kahlig1. (a) You are counting the number of games and thereare a limited number of games in a tennis match.Answer: Finite discrete(b) your counting the nubmer of tickets.Answer: Infinite discrete(c) Time is an interval and it doe sn’t skip values.Answer: Continuous(d) The number may be very large(hopefully), but it isstill only a fixed number.Answer: Finite discrete(e) Temperature is an interval and it doesn’t skip va l-ues.Answer: Continuous2. (a) There are 52 − 13 = 39 non-hea rt cards in a deck,so the maximum number of cards you could drawis 39 without drawing a heart. So the worst casescenario is 40 cards drawn.Answer: Finite discrete.Values: X = 1, 2, ..., 40(b) ContinuousValues: {x = time in hours |0 ≤ X ≤ 24}(c) You could always roll a one, so it might not happenthat you roll a six.Answer: Infinite discreteValues: X = 1, 2, 3, 4, ...3. The areas of the recta ngles must add to one since therectangles represent probability. The missing rectanglehas an area of 0.15.Answer: 0.15 + 0.2 + 0.3 = 0.65 or 1 −0.1 −0.25 = 0.0654. Let P (X = 6) = J then P (X = 3) = 2J0.1 + 0 .25 + P (X = 3) + 0.2 + 0.15 + P (X + 6) = 1 (fromthe histogram).P (X = 3) + P (X + 6) = 0.32J + J = 0.3and get J = 0.1Answer: 0.45 = P (X = 4) + P (X = 5) + P (X = 6)5. (a) Divide the frequency by the to tal number of stu-dents who have waited to ge t r e lative frequency( orprobability).students 0 1 2 4 6prob.4251025525425225(b) probability histogram0.60.40.51234 5678−10.10.20.36. There are a total of 7 cards that will be made. Three ofthem will have a word with three letters: Get, Its, fun.Answer:(a)letters 3 4 5 6prob.37172717(b) probability histogram1/71234 5678−15/74/73/72/77. (a) There can be different answers depending whereyour intervals star t.speed(x) freq25 ≤ x < 30 630 ≤ x < 35 735 ≤ x < 40 940 ≤ x < 45 845 ≤ x < 50 550 ≤ x < 55 5(b) prob dist.speed(x) prob25 ≤ x < 30 6/4030 ≤ x < 35 7/4035 ≤ x < 40 9/4040 ≤ x < 45 8/4045 ≤ x < 50 5/4050 ≤ x < 55 5/408. (a) frequency table141 homework problems, 12B-copyright Joe Kahlig Chapter 8 Solutions, Page 2grade(x) freq90 ≤ x ≤ 99 1080 ≤ x ≤ 89 1170 ≤ x ≤ 79 1160 ≤ x ≤ 69 1050 ≤ x ≤ 59 740 ≤ x ≤ 49 430 ≤ x ≤ 39 3(b) prob dist.grade(x) freq90 ≤ x ≤ 99 10/5680 ≤ x ≤ 89 11/5670 ≤ x ≤ 79 11/5660 ≤ x ≤ 69 10/5650 ≤ x ≤ 59 7/5640 ≤ x ≤ 49 4/5630 ≤ x ≤ 39 3/569. Remember that the remainder is what is left over afterperforming long division(by hand). For example: 7 di-vide by 3 has a remainder of 1 since 3 goies into 7 twotimes(this gives 3 ∗ 2 = 6) and 1 will be left over.remainder 0 1 2prob.28383810. The tree shows the exp eriment. Notice the tree stops onthe third level since either a head is tossed or the coinhas been tossed three times.HT1/32/3HH1/31/3TT2/32/33 Tosses3 Tosses1 Toss2 TossesUse the branches to get the probability.Answer:tosses 1 2 3prob.13294911. (a) P (X = 0) =C(4,0)C(48,3)C(52,3)(b) P (X = 2) =C(4,2)C(48,1)C(52,3)12. (a) P (X = 2) =C(5,2)∗C(7,1)C(12,3)=70220(b) P (X ≤ 2) =C(5,0)∗C(7,3)C(12,3)+C(5,1)∗C(7,2)C(12,3)+C(5,2)∗C(7,1)C(12,3)=210220orP (X ≤ 2) = 1 − P (X = 3) = 1 −C(5,3)∗C(7,0)C(12,3)13. (a) E(x) = 1 ∗ 0.3 + 2 ∗ 0.15 + 4 ∗ 0.35 + 5 ∗ 0.2 = 3(b) histogram0.11234 567−10.50.40.30.214. To calculate P (X = 70) remember that the probabilitiesmust add to 1.E(X) = 30 ∗0.31 + 32 ∗0.25 + 46 ∗0.29 + 49 ∗0.06 + 63 ∗0.04 + 70 ∗ 0.05 = 39.615. (a) Write out the cards and give the s c ore to each card.Note: the order of the numbers is not important.Card ScoreCard Score Card Score1,2 1 1,3 1 1,4 101,5 1 2,3 10 2,4 22,5 2 3,4 3 3,5 34,5 4Answer:score 1 2 3 4 10probability310210210110210(b) E(x) = 1 ∗310+ 2 ∗210+ 3 ∗210+ 4 ∗110+ 10 ∗210= 3.716. The proba bilities may be computed using a tree or com-binations.(a)hearts 0 1 2probability19341334234(b) E(x) = 0 ∗1934+ 1 ∗1334+ 2 ∗234= 0.517. Use a dice chart to find the probabilities.123456123456Red DieGreen Die1 2223 3 33344444445 5 5 5 5555566666666666(a)hearts 1 2 3 4 5 6probability1363365367369361136(b) E(x) = 1 ∗136+ 2∗336+ 3∗536+ 4∗736+ 5∗936+ 6∗1136E(X) = 4.47222141 homework problems, 12B-copyright Joe Kahlig Chapter 8 Solutions, Page 318. Note: X is the net winnings.(a)X 1999 499 99 24 −1probability15001500350010500485500(b) 5.119. X = profit on a chip.X 18 -23prob. 0.95 0.05Answer: E(x) = 18 ∗ 0.95 + (−23) ∗ 0.05 = 15.9520. X is your net winnings.hearts −5 −4 −1 4probability18383818E(X) = (−5) ∗ 1/8 + (−4) ∗3/8 + (−1) ∗ 3/8 + 4 ∗ 1/8E(X) = −221. Use a tree to set up the probability distribution.net winnings−1.50−0.500.501.502.50H3/7T4/714231/41/41/41/4(a)X -1.5 -.5 .5 1.5 2.5prob47328328328328(b) E(x) = −.43 so the game is not fair.22. Use a tree or combinations to find the probabilities.X is your net winning s and A be the cost of the game.1 red 2 red 0 redX 4-A 3 A- A 0-Aprob20366361036If the game is fa ir then E(x) = 00 =2036∗ (4 − A) +636∗ (2A) +1036∗ (−A)0 = 20(4 − A) + 1 2A − 10A18A = 80A =8018= 4.44So to make it fa ir(or as fair as possible) charge $4.44.23. X is the your net winnings.X 2 1 −3prob.161646(a) −1.5(b) No, the expected winnings are negative. For thisproblem the game favors the pers on running thegame.(c) Let A =Price of the g ame, then solve the followingequaiton,X 7 − A 6 − A 2 − Aprob.1616460 = (7 − A) ∗ 1/6 + (6 − A) ∗ 1/6 + (2 − A) ∗ 4/60 = (7 − A) + (6 − A) + (2 − AA) ∗ 4A = 3.5Answer: $3.5024. (a) X is the revenue at each locatio n.Location AX 4.5 4 6.5prob. 0.5 0.2 0.3Location BX 4.5 4 6.5prob. 0.25 0.2 0.55Expected value of each location:Location A: 4.5 ∗ 0.5 + 4 ∗ 0.2 + 6.5 ∗ 0.3 =$5Location B: 4.5 ∗ 0.25 + 4 ∗ 0.2 + 6.5 ∗ 0.55 = $5.5(b) Total revenue at location B is1500 ∗ 5.5 = 825 0more than82505= 1650 people25.77+4=71126.2323+15=233827. simplifyP (J)P (JC)=0.620.38=3119Answer: 31 to 1928. P (AC) =715+7=72229. P (E) =29and P (F ) =1029. Since E and F are indepen-dent, P (E ∩ F ) = P (E) ∗ P (F )P (E ∩ F ) =29∗1029=2026130. P (E) =214031. prob of 5th card is a heart given the information is1249Answer: 12 to 3732. Mean = 4.9Median = 5Mode = 633. Mean = 21.31 818Median = 20.5Mode = 19 and 2434. The fifth s core is less than or equal to 82 since 82 isthe median and there are 2 scores that are
View Full Document
Unlocking...