6.3 #1 - 12
1) Sample space 4C2 = 6. With one way for girls to be together, therefore 1/6
2) P(not same bday) = 364 x 363 x 362 x 361 x 360 x 359 x 358 / 365^7
= 0.926
P(A’) = 1 – 0.926 = 0.074
3)
a) 8C2 = 28
5C2 = 10
P(2red) = 10/28 = 5/14
b) 3C2 = 3
P(2green) = 3/28
p(not2green) = 25/28
34
67 but times 2 order can be switched
4) 7P2 = 42
12
23
45
56
6 pair of lanes. Therefore 12/42 = 2/7
5) all possible 18C3 = 816
a) 8C3 = 56
P(all runners) = 56/816 = 28/408 = 14/204 = 7/102
b) 6x4x8 = 192
p(1 of each) = 192/816 = 96/408 = 48/204 = 24/102 = 12/51 = 4/17
6)
All possible 16C2 = 120
White socks = 8C2 = 28
P(2white) = 28/120 = 14/60 = 7/30
7)
a) 9C2 = 36
8)
a) 5C2 = 10
3C2 = 3
P(2 girls) = 3/10
b) Order is important so 5! = 120 with one correct way
P(age) = 1/120
9)
20C4 = 4845
8C4 = 70
P(wingers) = 70/4845 = 14= / 969
b) no goalies or centres = 16C4 = 1001
1001/4845
10) 10 tickets are winners so divide by 10
P(1ticket) = 1/540000
P(10) = 10/540000 = 1/54000
P(100) = 100/540000 = 1/5400
b) 540000 x 0.05 = 27000
c) 540000 x 0.5 = 270000
11)
Suki all = 5c2 with suki on team 4c2
leo all = 4c2 with leo 3c2
All = 10
all = 6
with suki = 4
4/10
3/6
Multiply because mixed
12/60 = 1/5
12)
ai) 4 from buck = 22C4
4 from cross = 7C4
35 /7315
1/209
ii) at least so subtract from all possible
22-7 = 15
15C4 = 1365
with leo = 3
7315 – 1365 = 5950
P(atleast1) 5950 / 7315 = 170/209
b) choose subset of 2 so 7C2 = 42
one way for eldest then second eldest
P(a) = 1/42
6.4 Answers pg 334 # 1 – 7, 10
1a) Dependent
b) Independent
c) independent
d) Dependent
e) independent
f) dependent
2) .3 * .2 = 0.06 or 6%
3) 1/6 chance for any number. Rolled 5 times give (1/6)5 = 7776 But there are 6 numbers so 6/7776 = 1/1296
4.
a) 0.95 x 0.89 = 0.8455 = 84.55%
b) .05 x .11 = 0.0055 = 0.55%
c) at least so subtract from all possible (100%)
100% - 0.55% = 99.45%
5) Rocco 0.85 x 0.6 = 0.51 = 51%
Biff 0.7 x 0.75 = 0.525 = 52.5%
Therefore Biff more likely to enjoy the tasty treat!
6) 0.85 x 0.6 = 0.51 = 51%
7) 0.55 x (1/3) x 0.22 = 0.0403
OR
55/100 x 1/3 x 22/100
1210/30000 = 121/3000
10)
Pass data = 17/20
pass bio = 7/10
a) 17/20 x 7/10
b) 3/20 x 3/10
119/200
= 9/200
12) 30% of 26 does = 0.3 x 26 = 7.8
7.8/48 = 78/480 = 38/240 = 13/80
Chapter 6.5
1.
a) non – could be grey wool
b) non – could be honour kid with brown eyes
c) mut – can’t be even and odd
d) mut – 6 is not prime
e) non – sat is the weekend
f) non – an A is a pass
g) mut – stormy isn’t calm
h) non – could be both?
2)
a) 1/9
b) 3/9 = 1/3
c) 4/9
3)
a) 7%
b) 81%
c) 28 + 46 = 74%
d) 19 + 7 = 26%
4)
Jan – 31 F – 28 M – 31 A – 30 M – 31 J – 30 J – 31 A – 31 S – 30 O – 31 N – 30 D – 31
a) 31 + 31 + 31 + 31 = 124/365
b) 30 + 31 = 31 = 92/365
5)
No lake
lake
=220 - 110
=110
a) = 52/220
= 80 – 22
= 58
b) 80 /220
22
=52 - 22
= 30
c) 110/220
d) 30/220
6)
=800 - 250 =250+148 =200 - 148
=550
=398
=52
a) 550/1000 = 0.55
b) 148/1000 = 0.148
c) 550 + 398 = 948/1000 = 0.948
7)
a) 3/28
b) 16/28 = 8/14 = 4/7
c) 10 /28 = 5/14
10) 7 cross hatched bucks, so 7/48
Only does get bald patches. 30% of the 26 does have it, so 0.3 x 26 = 7.8
7.8/48 does
Since it says OR we add
7/48 + 7.8/48  Mult by to b/c of the decimal
70/480 + 78/480
= 148/480 = 37/120
11)
a) lock in hania (or Aaron) = 7! X 2 = 5040 * 2 = 10080
Hania first AND Aaron last = 6!=720
10080 – 720 = 9360
All possible = 8! = 40320
9360 / 40320 = 936/4032 = 468/2016 = 234/1008 = 117/504 = .232
b)
Hania first = 7! = 5040
Hania first & Aaron last = 720
d) 15/28
5040-720 = 4320
Prob = 4320/40320 = .107
13)
68
Calc
data
21
13
3
3
3
9
0
Geometry
b) 52/120 = 26/60 = 13/30
c) 24/120 = 2/10 = 1/5
6.6 pg 353 #1 – 4, 6 – 8, 10
1)
a) no – values do not add up to 1
b) yes
c) needs to be horizontal
d) no – add up to one, but cannot contain negative values
e) yes
2)
a) no – last row does not equal 1
b) yes
c) no – not square
3)
a) ZapShot has 67% market share. E-pics has 33%
b) The first row states that customers that try ZapShot 60% will return and 40% will try E-Pics.
The second row states that customers that try E-Pics 50% will return and 50% will try ZapShot.
0.67(0.6) + 0.33(0.5)
0.67(0.4) + 0.33(0.5)
= 0.408 +0.165
= 0.268 + 0.165
= 0.573
= 0.433
[0.573
0.433]
4)
a) ZapShot remains higher, so might stay higher.
b)
p = .6p + .5q
q = .4p + .5q
p - q = .2p
-q = .2p –p
-q = -.8p
Q = .8p
P+q=1
P +.8p = 1
1.8p = 1
P = 1/1.8 = 10/18 = 5/9
Therefore q = 4/9
[5/9
4/9]
c) E-Pics gained market share. From 33% to about 44%
d) they agree.
6)
a)
W
L
.7
.3 W
.4
.6 L
b) [.55 .45]
.565
.435
pg 357 #1 - 5, 6cd, 7 - 10, 13, 14a, 15-18
1.
a) 7/20
b) 15/20
2.
a) 5/20
b) 1/6
c) life happens
3)
a) 0% no going to happen
b) 100% we live in a snowy area. Bound to happen.
4.
1/8  1:7 odds
5.
a) 7:13
b) 10:10
c) 17:3
6.
c) 8C3/20C3 = 56/1140
d) 12C3/20C3 = 220/1140
7.
7!/9! = 5040/362880
8.
a) 5P3/10P3 = 60/720
b) 3P3/10P3 = 6/720
c) 1/720
9.
a) indep. Can’t bat and catch at same time
b) dep. Staying up late makes you want to sleep in.
c) dep. Doing review can help you do well (pass)
d) indep. Random, so not related.
10.
a) .4 x .75 = 0.3
b) Subjective. Percents are his opinion.
13.
a) exc. Different music
b) exc. Wednesday is not on the weekend
c) non-exc. Can have cheese and no onions
d) non-exc. Example – 36 is both
14.
a) 26 black plus 2 red 5. 28/52 =
15.
a)
14
Blonde
5
b) 8/26 = 4/13
glasses
4
3