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Math 166 WIR, Spring 2011, Benjamin
Aurispa
Math 166 Exam 1 Review Answer Key
1. (a) P (c) = 0.18, P (e) = 0.15
(b) 0.34
(c) 0.67
(d) 0.85
(e) No, not all outcomes are equally likely.
2. (a) 0.3
(b) 0.6
(c) 0.7
(d) 0.1
(e) No, since P (E ∩ F ) 6= 0, or equivalently, E ∩ F 6= ∅
(f) No, since P (E ∩ F ) 6= P (E)P (F )
3. 0.76
32
40
16
40
12
40
4. (a)
(b)
(c)
=
=
=
4
5
2
5
3
10
(d) 1 to 7
5.
90
92
=
6. (a)
(b)
(c)
45
46
10
5
36 = 18
1
3
6 = 2
7
11
7. (a) 0.2
(b) 0.54
(c) 0
(d) 0.86
(e) 0.94
8. (a)
(b)
330
33
350 = 35
30
1
60 = 2
(c) Not independent since P (G ∩ U ) 6= P (G)P (U )
9.
54
1033
≈ 0.0523; See Full Solutions for Tree Diagram
10. See Full Solutions for Tree Diagram
(a) 0.7092
(b) 0.85
(c)
22
727
≈ 0.0303
11. (a) 0.000189
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Math 166 WIR, Spring 2011, Benjamin
Aurispa
(b) 0.168367
12. See Full Solutions for Tree Diagram
(a)
(b)
4
15
27
47
≈ 0.5745
13. (a) The set of all residents in College Station who were born in Texas and are students at TAMU,
or who do not attend TAMU but are at least 21 years old.
(b) B ∩ Ac ∩ T c
14. Shade regions b, c, and h
15. a = 110, b = 90, c = 135, d = 165
(a)
(b)
335
500
275
500
=
=
67
100
11
20
(c) YES, P (D ∩ F ) = P (D)P (F )
16. a = 30, b = 16, c = 26, d = 10, e = 25, f = 17, g = 29, h = 32
(a) 46
(b) 85
(c)
69
185
Size
Probability
17. (a)
(b)
525
900
18. (a)
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
=
S
M
L
XL
XXL
150
950
225
950
300
950
200
950
75
950
21
38
True
False
False
True
False
False
True
False
i. {b, c, f, g, i}
ii. {a, b, f, i, j}
(b)
19. (a) S = {Hh, Ht, Ch, Ct, D1, D2, D3, D4, S}
(b) E = {Ch, Hh}
(c) F = {D1, D3}
(d) G = {Ch, Ct, S}
(e) E and F are mutually exclusive; F and G are mutually exclusive
(f)
20. (a)
1
4
i. The average temperature in August is 95◦ and it either rained 10 days in August or August
does not have the highest monthly average temperature.
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Math 166 WIR, Spring 2011, Benjamin
Aurispa
ii. It did not rain 10 days in August, or both the average temperature in August is 95◦ and
August has the highest monthly average temperature.
(b)
i. ∼ (r ∨ q) ∧ p
ii. (p ∧ ∼ r) Y q
21. (a)
p
q
(∼ p ∧ q)∨ ∼ q
T
T
F
T
F
T
F
T
T
F
F
T
p
q
r
(p Y ∼ q)∧ ∼ (q ∨ r)
T
T
T
F
T
T
F
F
T
F
T
F
T
F
F
F
F
T
T
F
F
T
F
F
F
F
T
F
F
F
F
T
(b)
3