1.Algebra Booster

Probability 8.31
67. 4/35
68. (a)
m
69.
m +
70.
71.
6
n
n
C 3 ¥ [3 - 3.2 + 3]
n
6
9m
m + 8N
72. (d)
73. (a)
74. 1/2
75. 2p 2 – p 3
76. (d)
n
77.
10 2 12 6 11 1 12 6
C1¥ C1 C2 ¥ C4 C1¥
C1
C1¥
C5
◊ + ◊
12 18 12 18
C2 C6 C2 C6
79. (b)
80. 1/7
81 (b)
82. (a)
83. (b)
84. (c)
85. (c)
86. (d)
88. (i) a (ii) b (iii) b
89. (b)
91. (a, d)
92. (i) b (ii) d
94. (a)
95. (a, b)
HINTS AND SOLUTIONS
LEVEL I
1. Here, S = {HH, HT, TH, TT}.
Then,
(i) the probability of 2 heads = 1 4
(ii) the probability of exactly one head, i.e.
{HT, TH} is = 2 = 1 .
4 2
(iii) the probability of exactly two tails, i.e.
{TT} = 1 4 .
2. Here,
S = {HHH, HHT, HTH, THH,
TTT, TTH, THT, HTT}
Then
(i) the probability of exactly two heads, i.e.
{HHT, HTH, THH} = 3 8
(ii) the probability of at least two heads, i.e.
{HHT, HTH, THH, HHH} = 4 =
1
8 2
(iii) the probability of exactly one head, i.e.
{TTH, THT, HTT} = 3 8 .
3. Here, S = {(1, 1), (1, 2), (1, 3), ..., (6, 6)}
(i) Let A be the event, which shows the outcome, a
sum of 10 = {(4, 6), (6, 4), (5, 5)}
So, the probability of A,
3 1
PA= ( ) =
36 12
(ii) Let B be the event, which shows the outcome, a
sum of at least 9
={a sum of 9, 10, 11 and 12}
= {(3, 6), (6, 3), (4,5), (5, 4), (4, 6), (6, 4),
(5, 5), (5, 6), (6, 5), (6, 6)}
So, the probability of B,
10 5
PB ( ) = =
36 18
(iii) Let C be the event which shows the outcome, a
sum of even numbers
= {a sum of 2, 4, 6, 8, 10, 12}
= {(1, 1), (1, 3), (3, 1), (2, 2), (1, 5),
(5, 1), (2, 4), (4, 2), (3, 3), (2, 6),
(6, 2), (3, 5), (5, 3), (4, 4)
So, the probability of C,
18 1
PC ( ) = =
36 2
(iv) Let D be the event shows the outcome, a sum of
odd numbers
= {a sum of 3, 5, 7, 9, 11}
= {(1, 2), (2, 1), (1, 4), (4, 1), (2, 3), (3, 2),
(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3),
(3, 6), (6, 3), (4, 5), (5, 4), (5, 6), (6, 5)}
So, the probability of D,
18 1
PD ( ) = =
36 2
(v) Let E be the event. A sum of perfect numbers =
{a sum of 6}( since only two perfect number exist
from 1 to 100 natural numbers, say, 6 and 28}
= {(1, 5), (5, 1), (2, 4), (4, 2), (3, 3)}