ANSWERS

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