736 ANSWERS c 5 5 fAKN, ANK, KAN, KNA, NAK, NKAg i We know the members of squad A generally ran faster because their median time is lower. ii We know the times in squad B are more varied because their range and IQR is higher. a x = E103:51, s ¼ E19:40 6 a mean is 18:8, standard deviation is 2:6 a 120 students d 21 marks b b 13:6 to 24:0 b 65 marks e 73% of them b 0:22 3 a 43 days 4 a ¼ 0:089 2 a 0:487 i ¼ 0:047 b b 0:051 ii ¼ 0:186 iii 0:465 coin die a 3 die 1 spinner 2 1 c b H T d spinner 1 spinner 2 X 1 Y Z X 2 Y Z X 3 Y Z B C D coin spinner A B H C A B T C T T coin H 1 4 1 1 4 b c a 1 36 25 36 b g 1 a 0:476 2 a 7510 1 2 3 4 d 1 18 1 6 draw 1 B W 3 a 0:428 h cyan d 6 7 36 49 1 a b 3 a 0:0096 5 a 0:56 6 a c d b 1 a 3 a c 4 a 14 55 4 5 e 1 36 c 0:758 a b 0:8096 4 a 12 125 c 0:14 e magenta e j ii iv 1 5 3 5 5 18 13 18 d 0:578 e 0:415 d 0:257 e 0:480 1 8 1 16 1 8 b b 15 16 c 7 15 1 f 1 18 3 100 3 100 a 7 15 b 3 2 £ 99 ¼ 0:0006 100 2 1 £ 98 ¼ 0:000 006 99 7 30 b £ 4 7 b a d 97 100 £ 96 99 £ 95 98 ¼ 0:912 2 7 1st spin 8 15 2nd spin f Qw_ R Qr_ Qr_ Y Qw_ Qr_ 95 100 50 75 25 0 Qr_ 5 95 yellow Qr_ Qr_ Qw_ 1 6 100 50 d 0:24 EXERCISE 15F 1 5 75 25 0 5 95 11 36 2 9 1 10 3 5 27 125 c 2 fremember leap yearsg 100 50 d 75 c 237 1461 i 5 ii 0:653 iii 0:243 2 1 55 b Qr_ 124 1461 i 216 343 c b 0:06 8 125 Qr_ 4 9 4 c d c 0:483 i 0:325 b 0:240 1 3 ii 1 9 1 3 0 b 2 3 i 2 7 7 15 3 EXERCISE 15E.2 draw 2 P B W P B W P B W P c 25 h 1 3 5 9 5 18 c B 5 a 50 25 0 5 4 b 95 a g 1 4 1 12 1 7 b 100 3 b a 4 75 2 1 5 2 b 10 b 0:241 b EXERCISE 15C.1 a spinner 10-cent Qw_ 1 a spinner 1 A 1 2 3 4 5 6 10-cent H 1 2 EXERCISE 15E.1 2 H 7 8 vi iii 3 5-cent iv H T 4 die 1 2 v T H 1 2 3 4 5 6 spinner 3 8 EXERCISE 15D d a 1 2 iii 2 f 1 2 3 4 5 6 c 3 1 2 ii T die 2 6 5 4 3 2 1 iv 5-cent b D C B A 1 8 iii 1 a 2 3 d EXERCISE 15C.2 b ¼ 0:126 T H 1 8 ii 1 2 i c 0:731 EXERCISE 15B 1 a fA, B, C, Dg b fBB, BG, GB, GGg c fABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BCAD, BCDA, BDAC, BDCA, CABD, CADB, CBAD, CBDA, CDAB, CDBA, DABC, DACB, DBAC, DBCA, DCAB, DCBAg d fGGG, GGB, GBG, BGG, GBB, BGB, BBG, BBBg 2 1 8 i b a 0:78 1 3 c a fABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BCAD, BCDA, BDAC, BDCA, CABD, CADB, CBAD, CBDA, CDAB, CDBA, DABC, DACB, DBAC, DBCA, DCAB, DCBAg 7 c 54 and 75 f 81 marks EXERCISE 15A 1 1 3 b a fGGG, GGB, GBG, BGG, GBB, BGB, BBG, BBBg 6 b ¹ = E103:51, ¾ ¼ E19:40 7 1 3 a black V:\BOOKS\IB_books\IB_SL-2ed\IB_SL-2ed_an\736IB_SL-2_an.CDR Monday, 30 November 2009 10:58:50 AM PETER B R Y B R Y B R Y b c d e 1 4 1 16 5 8 3 4 IB SL 2nd ed 737 ANSWERS 2 Qw_ win Qw_ lose Aw_p_ win 7 50 e no rain Rt_ 17 40 4 a 3 a 5 7 20 49 2 9 5 b 6 11 30 a 19 30 b 3 4 5 2 4 3 10 a 1 3 a 1 10 b 2 15 b 3 5 c 4 15 c 4 15 d These are all possibilities, so their probabilities must sum to 1. a 15 b 35 c 45 6 19 45 a 2 100 7 33 1 ¼ 0:0002 b 99 98 £ 97 ¼ 0:0398 100 99 98 100 £ c 1¡ 8 10 21 5 9 b A B A U B lose 9 38 EXERCISE 15G 1 f U Qw_Op_ 3 0:032 P(win) = rain Qt_ 97 99 £ a 29 a 65 a 19 40 b 17 b 9 b 12 c 26 c 4 c 45 d 5 d 52 d 58 19 25 7 15 13 25 1 15 6 25 2 15 7 19 6 7 6 a 7 a 8 a b b c c d d e 13 40 f 7 20 b ¼ 0:9602 A U B U A' is shaded. 9 7 to start with c A B A' Ç B is shaded. d EXERCISE 15H 1 2 a (p + q)4 = p4 + 4p3 q + 6p2 q 2 + 4pq3 + q 4 b 4( 12 )3 ( 12 ) = 14 i 5( 12 )4 ( 12 ) = iii 4 a ¡2 3 b i a ¡3 4 ¡ 1 ¢4 ¡ 1 ¢ 2 ¢ 1 4 + 3 + ¢ = = ii 10( 12 )2 ( 12 )3 = 1 32 ¡ 2 ¢4 3 +4 b = 1 5 4 i 10 = 16 81 ii 6 ¡ 3 ¢5 4 ¡ 3 ¢3 ¡ 1 ¢2 4 a ¼ 0:154 7 ¼ 0:000 864 ¡ 2 ¢3 ¡ 1 ¢ 3 4 3 +6 3 3 ¡ 2 ¢2 ¡ 1 ¢2 3 +5 3 = ¡ 3 ¢4 ¡ 1 ¢1 ¡ 3 ¢42 ¡ 1 ¢43 = 4 4 135 512 ii b ¼ 0:973 B U A B A' Ç B' is shaded. 9 a + 8 27 + 10 +5 53 512 A B b A B ¡ 2 ¢2 ¡ 1 ¢2 8 9 iii c ¡ 3 ¢3 ¡ 1 ¢2 ¡ 3 ¢ ¡41 ¢4 4 iii 4 C U 3 4 + A C U B d A B ¡ 1 ¢5 4 47 128 a ¼ 0:0305 6 8 ¼ 0:0341 5 16 ¡ 2 ¢ ¡ 1 ¢3 3 ¡ 1 ¢34 +4 ¡ 2 ¢4 3 2 5 32 +10 5 A A È B' is shaded. a (p + q)5 = p5 + 5p4 q + 10p3 q2 + 10p2 q 3 + 5pq 4 + q 5 b 3 U C U C U b ¼ 0:265 e 9 4 dice A B f A B EXERCISE 15I.1 b cyan 3 yellow b+c a+b+c+d a+b+c iii a+b+c+d a i b a+b+c+d a+b+c iv a+b+c+d ii 25 0 b P(A or B) = P(A) + P(B) ¡ P(A and B) 5 95 100 50 95 magenta B 75 A U 100 50 75 25 0 B 5 95 A 100 50 75 25 U 0 B d 25 c 5 A U 95 B 100 A C U EXERCISE 15I.2 1 For each of these draw two diagrams, shade the first with the LHS set and the second with the RHS set. 2 a A = f7, 14, 21, 28, 35, ......, 98g B = f5, 10, 15, 20, 25, ......, 95g i n(A) = 14 ii n(B) = 19 iii 2 iv 31 50 U C U 75 a 0 2 a A = f1, 2, 3, 6g, B = f2, 4, 6, 8, 10g b i n(A) = 4 ii A [ B =f1, 2, 3, 4, 6, 8, 10g iii A \B =f2, 6g 5 1 black Y:\HAESE\IB_SL-2ed\IB_SL-2ed_an\737IB_SL-2_an.CDR Tuesday, 17 March 2009 10:25:16 AM PETER IB SL 2nd ed 738 ANSWERS EXERCISE 15J 1 a 2 M 22 study both 9 ii b i 25 P 22 18 a 3 a 14 25 5 a 6 a 9 a 0:45 13 20 3 5 W' (0.64) b c d 15 23 b 4 5 c 1 5 d 5 23 b 7 20 c 11 50 d 7 a 0:0484 a 0:46 7 25 14 23 b e 9 14 e 4 7 4 5 6 f 1 4 W' (0.64) 5 1 ¡ 0:9 £ 0:8 £ 0:7 = 0:496 70 163 8 6 2 3 11 7 30 7 12 b a 0:35 14 15 7 10 c 7 d 0:15 1 8 5 8 c 3 a 2 5 b 13 15 b 5 + ¡ 2 ¢45 5 Male 40 70 110 Total 60 140 200 c ¼ 0:121 5 33 b 19 66 c 5 11 3 a 3 25 b 24 25 c 11 12 4 a 5 8 b 1 4 d 16 33 0:9975 W (0.95) W (0.95) W' (0.05) W' (0.05) 6 a 7 a 31 70 ¡4 ¢ 1 5 + 5 5 b = 21 31 ¡ 4 ¢5 5 +10 +5 ¡ 4 ¢4 ¡ 1 ¢ 5 ¡ 4 ¢2 ¡ 1 ¢3 5 5 5 +5 i ¼ 0:0205 + 10 ¡ 4 ¢3 ¡ 1 ¢2 ¡ 4 ¢ ¡ 1 ¢54 5 5 + ¡51 ¢5 5 ii ¼ 0:205 EXERCISE 16A die 1 37 40 c 2 5 8 5 9 a 7 2 a ¡3 b 6 c ¡8 d 3 a 0 b 3 c ¡ 23 d ¡1 R (0.6) N (0.4) yellow 50 25 0 5 95 100 50 25 0 5 95 100 50 75 25 0 5 95 100 75 75 R (0.6) R (0.6) magenta c 11 d 16 e 0 1 2 3 2 f g 5 1 2 f 5 e 1 f 1 e h ¡2 a vertical asymptote x = ¡3, horizontal asymptote y = 3 as x ! ¡3¡ , f (x) ! 1 as x ! 1, f (x) ! 3¡ as x ! ¡3+ , f (x) ! ¡1 as x ! ¡1, f (x) ! 3+ b horizontal asymptote y = 1: as x ! 1, y ! 1¡ as x ! ¡1, y ! 1¡ c horizontal asymptote y = 0: as x ! 1, f (x) ! 0+ as x ! ¡1, f (x) ! 0¡ 1 N (0.4) N (0.4) cyan b 7 EXERCISE 16B N (0.4) N (0.4) 95 b 1 100 1 4 R (0.6) 50 5 a R (0.6) 25 5 2 b REVIEW SET 15B 1 P(N wins) 44 = 125 = 0:352 0 Female 20 70 90 1 2 ii ¡ 3 ¢ ¡ 2 ¢3 ¡ 3 ¢2 ¡ 2 ¢2 W' (0.05) 1 2 3 4 5 6 5 7 20 i +6 328 625 ii W (0.95) 2 9 5 12 a die 2 5 5 4 15 a 0 b 0:45 c 0:8 a Two events are independent if the occurrence of each event does not influence the occurrence of the other. For A and B independent, P(A) £ P(B) = P(A and B) b Two events A and B are disjoint if they have no common outcomes. P(A or B) = P(A) + P(B) a 5 1 BBBB, BBBG, BBGB, BGBB, GBBB, BBGG, BGBG, BGGB, GGBB, GBBG, GBGB, BGGG, GBGG, GGBG, GGGB, GGGG. P(2 children of each sex) = 38 4 5 7 ¡ 3 ¢3 ¡ 2 ¢ REVIEW SET 15C a 6 5 4 3 2 1 c 216 625 i b 2 6 +4 5 a e 0:5 REVIEW SET 15A 1 ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BCAD, BCDA, BDAC, BDCA, CABD, CADB, CBAD, CBDA, CDAB, CDBA, DABC, DACB, DBAC, DBCA, DCAB, DCBA a 12 b 13 b ¡ 3 ¢4 = smoker non-smoker total 6 Hint: Show P(A0 \ B 0 ) = P(A0 ) P(B 0 ) using a Venn diagram and P(A \ B) 7 0:9 7 8 a i 13 ii 10 b No, as P(C \ D) 6= P(C) P(D) 20 3 8 ¢ 2 4 5 + 5 No, as P(A \ B) 6= P(A) £ P(B) b 0:85 c 0:15 91 a 216 b 26 5 ¡3 b 75 3 4 a a +4 EXERCISE 15K 1 P(R \ S) = 0:2 and P(R) £ P(S) = 0:2 ) are independent events 2 W (0.36) R' (0.75) c 0:65 b 0:3926 a 0:09 b 0:52 W (0.36) R (0.25) 1 5 b 0:75 b ¼ 0:703 4 7 20 2 3 b 3 2 £ 498 ¼ 0:000 000 193 499 496 495 £ 499 £ 494 ¼ 0:023 86 500 498 £ a ¼ 0:259 3 0 3 8 10 4 500 b 1¡ 11 20 10 U 2 a black Y:\HAESE\IB_SL-2ed\IB_SL-2ed_an\738IB_SL-2_an.CDR Wednesday, 18 March 2009 10:49:04 AM PETER IB SL 2nd ed