#4 # 4
47. m ! "
"
0#7
#8
!"
"
#7
8
! ""; perpendicular
7
2
2
6c. P(4 tails or 1 head)
! "1" % "1" % "1" % "1" % "1" % "1" % C(6, 4) $
slope !
2 2 2 2 2 2
1 1 1 1 1 1
"" % "" % "" % "" % "" % ""
2 2 2 2 2 2
!
!
! "1" "6"
$ "1" "6"
64 2!4!
64 5!1!
! "1"(15) $ "1"(6)
64
64
! "21"
64
#"7"
8
! "
48. 12a $ bc ! 12(3) $ (7)(#2)
! 12(9) $ (#14)
! 108 # 14
! 94
2 2 2 2 2 2
1 1 1 1 1 1
"" % "" % "" % "" % "" % ""
2 2 2 2 2 2
!
!
! "1" "6"
$ "1" "6"
64 0!6!
64 0!6!
! "1" $ "1"
64
64
! "2" or "1"
64
32
! "
Page 748 Check for Understanding
1. Mutually exclusive events cannot occur at the
same time, whereas inclusive events can.
2. Sample answer: going to school, eating pizza, or
watching TV.
3. 134 # 62 !72
Glass
Aluminum
108 # 62 !46
72
26
8. P(French or algebra)
9
52
2
""
13
! "5"
9
9
10. inclusive;
2
P(black card or face card) ! "26" $ "1"
# "6"
52
52
8
""
13
! "32" or
52
52
11. inclusive;
P(tossing 5 or number greater than 3) ! "1" $ "3" # "1"
52
6
! "3" or
6
! "
34
! "21"
34
34
34
C(4, 2) % C(5, 1)
! "
6%5
!"
"
84
C(9,3)
! "30" or
84
5
""
14
14. P(all 3 gold or all 3 silver) ! P(3 gold) $ P(3 silver)
C(5, 3)
C(4, 3)
! "" $ ""
C(9, 3)
! "10" $ "4"
84
! "14" or
% C(6, 2)
84
! "
© Glencoe/McGraw-Hill
6
13. P(exactly 2 silver) ! ""
6b. P(3 tails or 2 heads)
! "1" % "1" % "1" % "1" % "1" % "1" % C(6, 3) $
2 2 2 2 2 2
1 1 1 1 1 1
"" % "" % "" % "" % "" % ""
2 2 2 2 2 2
!
!
! "1" "6"
$ "1" "6"
64 3!3!
64 4!2!
! "1"(20) $ "1"(15)
64
64
! "35"
64
6
1
""
2
12. inclusive;
1
P(boy or a senior) ! "14" $ "1"
# "4"
2 2 2 2 2 2
1 1 1 1 1 1
"" % "" % "" % "" % "" % "" % C(6, 5) $
2 2 2 2 2 2
1 1 1 1 1 1
"" % "" % "" % "" % "" % "" % C(6, 6)
2 2 2 2 2 2
!
!
!
! "1" "6"
$ "1" "6"
$ "1" "6"
64 2!4!
64 1!5!
64 0!6!
! "1"(15) $ "1"(6) $ "1"(1)
64
64
64
1
! "22" or "1"
64
32
! "
26
550
700
400
! "" $ "" # "
"
1400
1400
1400
850
! ""
1400
! "17"
28
9. mutally exclusive;
P(physics book or history book) ! "3" $ "2"
6a. P(at least 4 heads)
! P(4 heads) $ P(5 heads) $ P(6 heads)
! "1" % "1" % "1" % "1" % "1" % "1" % C(6, 4) $
! "
26
Pages 749–751 Exercises
or
5b. inclusive;
P(jack or diamond)
! P(jack) $ P(diamond) # P(jack and diamond)
3
! "4" $ "1"
# "1"
52
or "4"
13
! "
! "8"
46
52
! "8"
52
% C(6, 6)
7. P(vowel or letter from equation) !"5" $ "3"
4a. The events are not mutally exclusive.
4b. probability of rain on both days
5a. mutually exclusive; P(5 or ace) ! P(5) $ P(ace)
! "4" $ "4"
52
! "16"
52
! "
6d. P(all heads or all tails)
! "1" % "1" % "1" % "1" % "1" % "1" % C(6, 6) $
12-6 Adding Probabilities
Alum.
and
Glass
62
% C(6, 1)
C(9, 3)
84
1
""
6
15. P(at least 2 gold) ! P(2 gold) $ P(3 gold)
C(5, 2) % C(4, 1)
C(5, 3) % C(4, 0)
! "" $ ""
C(9, 3)
10 % 4
10 % 1
!"
" $ ""
84
84
0
! "40" $ "1"
84
84
5
! "50" or "2"
84
42
345
C(9, 3)
Algebra 2 Chapter 12
16. P(at least 1 silver)
! P(1 silver) $ P(2 silver) $ P(3 silver)
C(4, 1) % C(5, 2)
C(4, 2) % C(5, 1)
24. P(at least 3 women)
! P(3 women) $ P(4 women) $ P(5 women)
C(4, 3) % C(5, 0)
C(7, 3) % C(6, 2)
C(9, 3)
C(9, 3)
4 % 10
6%5
4%1
!"
" $ "" $ ""
84
84
84
0
! "40" $ "3"
$ "4"
84
84
84
7
! "74" or "3"
84
42
C(9, 3)
25.
17. P(both kings or both black)
! P(both kings) $ P(both black) # P(both black kings)
6 25
! "4" % "3" $ "2"
% "" # "2" % "1"
52 51
52 51
52
2
650
2
! "1"
$"
" # ""
2652
2652
2652
660
55
!"
" or ""
2652
221
26.
51
27.
18. P(both kings or both face cards)
! P(both kings) $ P(both face cards) # P(both kings)
2 11
! "4" % "3" $ "1"
% "" # "4" % "3"
52
51
52
51
2
132
12
! "1"
$"
" # ""
2652
132
!"
"
2652
2652
1
or "1"
221
52
51
28.
2652
52
52
52
51
2652
752
!"
" or
2652
2652
188
""
663
52
51
2652
20. P(both either red or a king)
! P(both red or both kings)
$ P(red but not a king, 1 king)
! [P(both red) $ P(both kings)
C(24, 1) % C(4, 1)
# P(both red kings)] $ ""
#
26 25
4
"" % "" $ ""
52 51
52
5
6
! "5"
$ "9"
2 21
1326
426
71
!"
" or ""
1326
221
!
$
C(52, 2)
24 % 4
% "3" # "2" % "1" $ "
"
51
52
51
1326
21. P(4 women, 1 man or 4 men, 1 woman)
! P(4 women, 1 man) $ P(4 men, 1 woman)
C(7, 4) % C(6, 1)
C(6, 4) % C(7, 1)
C(13, 5)
C(13, 5)
1287
315
!"
" or
1287
1287
35
""
143
22. P(3 women, 2 men or 3 men, 2 women)
! P(3 women, 2 men) $ P(3 men, 2 women)
C(7, 3) % C(6, 2)
C(6, 3) % C(7, 2)
! "" $ ""
C(13, 5)
35 % 15
20 % 21
!"
" $ ""
1287
1287
945
105
!"
" or ""
1287
143
C(13, 5)
flat
26
round
flat
round
flat
round
flat
round
flat
round
flat
32b. P(advancing 2 lines) ! "1"
8
23. P(all women or all men)
! P(all men) $ P(all women)
P(advancing 1 line) ! "1"
8
P(advancing at least 1 line) ! "1" $ "1"
C(6, 5) % C(7, 0)
C(7, 5) % C(6, 0)
! "" $ ""
C(13, 5)
C(13, 5)
6%1
21 % 1
!"
" $ ""
1287
1287
7
! "2"
or "3"
1287
143
© Glencoe/McGraw-Hill
% "1"
6000
! 52% $ 74% # 30%
! 96%
32a.
round
round
flat
! "" $ ""
35 % 6
15 % 7
!"
" $ ""
C(13, 5)
C(13, 5)
C(13, 5)
35 % 15
35 % 6
21 % 1
! "" $ "" $ ""
1287
1287
1287
756
84
! "" or ""
1287
143
P(each is a 25) ! "1" % "1"
30 26
! "1"
780
9 25
P(neither is a 20) ! "2"
% ""
30 26
145
!"
"
15 6
6
0
P(at least one is a 30) !"1" % "2"
$ "3"
% "1" # "1"
30 26
30 26
30
26
30
1
! "" $ "" # ""
780
7 80
780
5
1
! "5"
or "1"
780
156
P(each is greater than 15) ! "15" % "26"
30 26
! "1"
2
29. P(A), P(B), P(C), P(A and B), P(B and C),
P(A and C), P(A and B and C);
P(A or B or C) ! P(A) $ P(B) $ P(C)
# P(A and B) # P(B and C) # P(A and C)
$ P(A and B and C)
30. Sample answer: Let A stand for a white counter
in the bag in the beginning, B for a black counter,
and C for the added white counter. After a white
counter is taken, there are three equally possible
situations:
1. C has been taken, leaving A.
2. A has been taken, leaving C.
3. C has been taken, leaving B.
Since a white counter remains in the bag for the
first two cases and a black counter remains in the
third case, the answer is therefore "2".
3
31. P(woman or person in his or her 20s)
! P(woman) $ P(person in his or her 20s)
# P(woman in 20s)
1800
! 52% $ 74% # "
"
19. P(both face cards or both red)
! P(both face cards) $ P(both red)
# P(both red face cards)
6 25
! "12" % "11" $ "2"
% "" # "6" % "5"
132
650
30
!"
" $ "" # ""
C(7, 5) % C(6, 0)
C(7, 4) % C(6, 1)
! "" $ "
" $ ""
! "" $ "" $ ""
8
8
! "1"
P(losing a turn) ! "6" or
8
346
3
""
4
4
Algebra 2 Chapter 12
33a.
First
Serve
Second
Serve
Point
in
80%
yes
no
yes
no
75%
25%
90%
out
10%
20%
in
out
40. M&1 " $1$
&21 ! 25
35%
65%
4
" 35 &57 # # " xy # " " 48 #
"
1 &7 5
$$
4 &5 3
0.75(0.80) ! 0.25(0.90)(0.35)
34b.
34c.
34d.
35a.
" 0.8839779 or about 88.4%
P(being intoxicated and having an
unimpeded trip) "
0.02 # 0.99911 " 0.0199822
P(being unintoxicated and having an
unimpeded trip) "
0.98 # 0.99984 " 0.9798432
P(being intoxicated, arrested, and convicted) "
0.02 # 0.00044 # 0.70 " 0.00000616
P(being intoxicated, arrested, and dismissed) "
0.02 # 0.00044 # 0.30 " 0.00000264
P(1 red gumball, then another red gumball,
then another red gumball) " $7$ % $6$ % $5$
36
35
210
"$
$ or
42840
36
35
42840
" xy # " $14$" 124 #
" xy # " " 31 #; (3, 1)
36
35
36.
37.
42840
d " 15 & 6 or 9
a57 " 6 ! (57 & 1)9
" 510
3x ! 5
$$
3x ! 1
&2
3 ! $3x$
"
1 & 2x
34
1
$$
204
Pages 755–756 Check for Understanding
1. A binomial experiment exists if and only if these
conditions occur.
a. There are exactly 2 possible outcomes for any
trial.
b. There is a fixed number of trials.
c. The trials are independent.
d. The probability of each trial is the same.
2.
S
S
M
S
S
M
M
S
S
S
M
M
S
M
M
S
S
M
S
S
M
M
M
S
S
M
M
S
M
M
3. Sample answer: coins, dice, spinners, random
draws from a bag
4. See students’ work.
5. The results will be closer to the theoretical
probability.
6a. (G ! W )4 " G4 ! 4G3W ! 6G2W 2 ! 4GW 3 ! W 4
P(at least one white)
" 4G3W ! 6G2W 2 ! 4GW 3 ! W 4
34
1
$$
119
"
34
3
$$
340
3x ! 5
2(3x ! 1)
$$ & $$
3x ! 1
3x ! 1
3(1 & 2x)
$$
1 & 2x
! $3x
$
1 & 2x
3x ! 5 & 6x & 2
$$
3x ! 1
3 & 6 x ! 3x
$$
1&2x
&3x ! 3
1 & 2x
"$
$ # $$
3x ! 1
&3x ! 3
1 & 2x
"$
$
3x ! 1
38. f(x) "&3x3 ! 2
f(2) " &3(2)3 ! 2
" &22
39a. a " 23, b " 48
y2
x2
$$ ! $$ " 1
2304
Binomial Experiments and
Simulations
12-7
35c. P(1 white gumball, then another white gumball,
then 1 purple gumball) " $7$ % $6$ % $9$
378
"$
$ or
x
&7 5
#
" $1$"
# # " 35 &5
# # " 48 #
&7 # " y #
4 &5 3
! 40
" xy # " $14$" &28
&20 ! 24 #
35b. P(1 purple gumball, then 1 orange gumball,
then 1 yellow gumball) " $9$ % $8$ % $5$
360
"$
$ or
5
" &7
#
&5 3
" $1$
33b. 0.75(0.80) ! 0.25(0.90)(0.35)
" 0.67875 or about 67.9%
0.75(0.80)
33c. $$$$
34a.
5
" &7
&5 3 #
529
39b. The desk is at one focus point.
c2 " 2304 & 529
c2 " 1775
c ! 42
He had to stand about 84 feet away.
"4
$$34$% $$14$% ! 6$$34$% $$14$%
3
2
2
7
" $27$ ! $2$
! $3$ ! $1$
64
175
"$
$
128
64
$$34$%$$14$%
!4
3
!
$$14$%
4
256
256
! 0.6836 or about 68.4%
© Glencoe/McGraw-Hill
347
Algebra 2 Chapter 12