MATH 119 FINITE MATHEMATICS
SPRING 2009 TEST 2
NAME ____________________________
Please show all necessary work. Feel free to ask me questions. Feel free to use any of the formulas
given on the last page. If you use a formula, tell me which one you're using before you plug your
numbers in.
1. 12 years ago, Carol invested money into an account with an APR of 3.8% compounded monthly. If
the balance is now $34,685.51, how much was her initial investment?
2. When my daughter was born 5 years ago, we started a savings account for her. We put $50 in
every month. If the account has an APR of 2.9%, how much will be in the account when my
daughter turns 18?
3. My roommate in college bought a used car at a pretty shady dealership. When he financed
through the dealership, his monthly payments were $139.58 with an interest rate of 13.99% for a
five year loan. What was the original price of the car?
Bonus) As it turns out, my roommate ran out of cash about half way through the loan, so he put
all of his payments for 2 ½ years on his credit card, which had an APR of 21.99%. If he was able to
pay off the credit card at the end of the five years, how much would he have paid, total, for the car?
4. Breny has $350,000 accumulated in her IRA, which earns 3.9% interest compounded monthly.
She draws $1900 from the account per month. How long will her retirement last?
5. Please fill in the first three lines of the following amortization table.
Loan amount = $240,000
APR = 5.5% compounded monthly
Term = 30 years
Monthly payment = __________________
Time
0
1
2
Payment
Payment to Interest
Payment to Principal
Balance
6. Let A  {1,3,5,7,9} , B  {2,4,6,8} , and C  {1,2,3,4,5,6} . List all of the elements in the following sets.
A B 
B C 
A B C 
7. Let A be the set of NAU students who have a Wii, let B be those students who are currently
enrolled in a Math class, and C be students who are vegetarian. Write a set notation description
(something like A  B  C ) for the sets described below.
a) non-vegetarians who don't have a Wii
b) students in a math class who have a Wii or who are vegetarian
c) vegetarians without Wiis who are not in a math class
8. A survey of 200 college students reveals that 83 own cars, 97 own bikes, 28 own motorcycles, 53
own a car and a bike, 14 own a car and a motorcycle, 7 own a bike and a motorcycle, and 2 own all
three.
a) Fill in every region of this Venn diagram.
b) How many only use two-wheeled transportation?
c) How many have a bike only?
d) How many don't have any of these types of transportation?
Compound interest A  P(1  i) n
 (1  i)n  1
Future value of annuity S  R 

i


Continuous compound interest A  Pe rt
1  (1  i)  n 
Present value of annuity P  R 

i


Pi
Regular amortization payment R 
1  (1  i )  n
| A B | | A|  | B | | A B |
| A B C | | A|  | B |  |C | | A B | | B C | | AC |  | A B C |
MATH 119 FINITE MATHEMATICS
SPRING 2009 TEST 3
NAME ____________________________
Please show all necessary work. Feel free to ask me questions. Feel free to use any of the formulas
given on the last page. Unless otherwise stated, you can stop once your answer is in terms of
factorials. You must provide explanation for your answers if you hope to get partial credit.
1. (6) How many license plates can be made using 4 letters followed by 3 digits?
2. Suppose you flip a coin three times.
a) (5) Describe the sample space of this experiment. Include its size.
b) (12) For each of the following events, give a few examples of outcomes within the event and
calculate the event's probability.
A: heads first (anything second and third)
B: exactly two tails
C: at least one heads
3. (12) I've been looking online for houses for sale in Flagstaff lately. From what I've seen, 33% have
garages, 22% have driveways that face south, and 8% have garages and driveways that face south.
What's the probability that a house for sale has
a) a garage or a driveway facing south?
b) neither a garage nor a driveway facing south?
c) a driveway facing south, but no garage?
4. (15) My daughter's Easter candy included 7 chocolates, 9 Starbursts, and 6 lollipops. While she
was taking a nap, I grabbed 5 pieces of candy. What is the probability that
a) 3 are Starbursts?
b) 2 are chocolates and 2 are lollipops?
c) at least 1 is a chocolate?
5. (9) Find each probability by referring to the tree below.
0.6
0.2
A
X
P( B | X ) 
P ( A) 
B
A
Y
0.7
B
P (Y  B ) 
6. (7) 2 cards are drawn from a standard deck of 52 without replacement. What is the probability
that the first is a heart and the second is red?
7. (10) You ask a neighbor to water a sickly plant while you are on vacation. Without water, the
plant will die with probability 0.9. With water, it will die with probability 0.55. You are 80%
certain the neighbor will remember to water the plant. You come back and the plant is dead.
What is the probability that the neighbor watered the plant?
8. (10) Roscoe makes up a game where his roommate rolls two dice and Roscoe pays him twice the
difference between the two dice (i.e. if his roommate rolls a 2 and a 6, Roscoe pays him $8). If
Roscoe charges his roommate $5 each time he rolls, how much money can Roscoe expect to make
per roll?
You may find this table helpful:
1
2
3
4
5
6
1
0
1
2
3
4
5
2
1
0
1
2
3
4
3
2
1
0
1
2
3
4
3
2
1
0
1
2
5
4
3
2
1
0
1
6
5
4
3
2
1
0
9. (14) Make a histogram and find the variance of the following distribution. Also, comment on the
relationship between your histogram and the value you get for variance.
X
4
8
12
16
20
P(n, r ) 
P(X)
0.2
0.15
0.1
0.3
0.25
n!
(n  r )!
P(not A)  1  P( A)
C (n, r ) 
n!
(n  r )!r!
P( B | A) 
P( A) 
P( B  A)
P( A)
| A|
|S|
P( A  B)  P( A)  P( B)  P( A  B)
P( B  A)  P( A) P( B | A)
E ( X )  X 1P( X 1 )  X 2 P( X 2 )  X 3 P( X 3 )    X n P( X n )
Var ( X )  P( X 1 )( X 1  E ( X )) 2  P( X 2 )( X 2  E ( X )) 2  P( X 3 )( X 3  E ( X )) 2    P( X n )( X n  E ( X )) 2