c
Math 166 WIR, Spring 2011, Benjamin
Aurispa
Math 166 Final Exam Review Answer Key
1. (a) Regular
(b) Absorbing
(c) Neither
2. (a) 4 months later, 44.07% will buy Coke, 31.14% will buy Pepsi, and 24.79% will buy Dr. Pepper
(b) 0.1874


127/281
(c) X =  91/281 
63/281

1 0 3/7 29/49
 0 1 4/7 20/49
3. L = 
 0 0 0
0
0 0 0
0




In the long run, if you start in state C, the probabilities are 73 and 74 that you will eventually be
20
absorbed by states A and B respectively. If you start in state D, the probabilities are 29
49 and 49 that
you will eventually be absorbed by states A and B respectively.
3
32 7
4. 11
t − 11
, 11 t + 17
,
t
, where t is any real number.
11
5. a = 26, b = −13, c = 4, d = 9
6. (a) $1140.41
(b) $165,123
(c) $255.41
(d) $58,988.35
7. 250,000
8. a = 25, b = 31, c = 45, d = 11, e = 73, f = 42, g = 30, h = 43
(a) 160
(b) 145
(c)
9.
84
300
=
7
25
13
60
10. (a)
(b)
(c)
(d)
29
35
29
35 ; 29 to
4
1
20 = 5
8
4
22 = 11
6
(e) Not mutually exclusive since E and F CAN occur at the same time.
(f) Yes, they ARE independent since P (E ∩ F ) = P (E) · P (F ).
11. (a) 6,012,580
(b) 0.8777
1
c
Math 166 WIR, Spring 2011, Benjamin
Aurispa
12. (a)
693
5512
≈ 0.1257
(b) They are NOT independent since P (D ∩ F ) 6= P (D) · P (F ).
13. −$0.28
14. 0.0033
15. (a) 2,592,000
X
Prob
(b)
0
1
2
11
24
11
24
1
12
16. (a) 5 years
(b) $5135.96
(c) $51.79
17. (a) E = {1A, 1Ac , 2A, 2Ac , 3A, 3Ac , 4A, 4Ac }
(b) No, not all outcomes are equally likely
(c) E = {1A, 2A, 3A, 3Ac , 4A}
(d)
6
13
18. (a) 0.2023
(b) 12,844.0386 pounds
19. (a) {2, 4}
(b) {1, 2, 3, 4, 6}
(c) False
(d) False
(e) True
20. Regions a, b, c, f, and h are shaded
21. 360,360
22. (a) X = Number of Cheetos
(b) Mean = 105.1765, Median = 100, Mode= 95, σ = 9.0569, V ar(X) = σ 2 = 82.0277
23. (a) The Aggies are going to the Cotton Bowl and beat Oklahoma, or they did not beat Missouri.
(b) (r∧ ∼ p) Y (q ∧ ∼ p)
(c) See Full Solutions
24. (a) X = 1, 2, 3, 4, . . .; X is Infinite Discrete
(b) X = 0, 1, 2, . . . , 12; X is Finite Discrete
(c) X = 1, 2, 3, . . . , 40; X is Finite Discrete
25. 2 goldfish, 48 tetras, 24 guppies
26. 9.5%
27. (a) 0.1106
(b) 6
2
c
Math 166 WIR, Spring 2011, Benjamin
Aurispa
28. $5971.46; Interest is $1028.54
29. (a) 2 × 2
(b) Not Possible
(c) Not Possible
30. 4,968,000
3