MAT 170

1. Find the probability. Assume that the spinner is separated into equal sections:
You flip a coin and toss a 1-6 number cube.
P(3 and heads)
P(3 and heads) = P(3) * P(head) = 1/6 * ½ = 1/12 = 0.083

A)
0.083
B)
0.167
C)
0.125

2. Evaluate the expression: 6! + 4!
6! + 4! = 6*5*4*3*2*1 + 4*3*2*1 = 720 + 24 = 744
A) 744
B) 704
C) 720

3. Evaluate the expression: P(5,5)

P(5, 5) = 5!/0! = 5*4*3*2*1/1 = 120
A) 120
B) 230
C) 25

4. If A and B are independent events, P(A)=.4, and P(B)=.6 find
P(A ∩ B) = P(A)*P(B) = 0.4*0.6 = 0.24
P(A U B) = P(A) + P(B) – P(A ∩ B) = 0.4+0.6 – 0.24 = 0.76
A) 0.76
B) 0.076
C) 0.0076

5. State whether the statements are true or false:

A) True
B) False

6. Evaluate: 3!
3! = 3*2*1 = 6
A) 6
B) 3
C) 1

7. Using the combination formula complete the following:
How many combinations of two letters are possible from the letters U, A, and X?
Number of combinations = C(3, 2) = 3!/(2!*1!) = 3
A) 3
B) 5
C) 9

8. Evaluate the expression: 5!-3!
5!-3! = 120 – 6 = 114
A) 114
B) 2
C) 8

9. Evaluate the expression: C(9,3)
C(9, 3) = 9!/(3!*6!) = (9*8*7)/(3*2*1) = 84
A) 84
B) 48
C) 27

10. Fill in the missing value. Assume simple interest.
principal               $19,582
interest rate                  4%
time                    ________
simple interest     $2,349.84
I = prt
2,349.8 = 19582*0.04*t
t = 2,349.8 /(19582*0.04) = 2.99995
A) time 3 years
B) time 4 years
C) time 2 years

11. Evaluate the expression:
= 2* (7*6*5*4*3*2*1) = 10080
A) 10,080
B) 10,280
C) 10,000

12. Evaluate: 5!
5! = 5*4*3*2*1 = 120
A) 120
B) 25
C) 5

13. There were 13,249 weddings in Springs City last year. According to state records, notaries public performed 17% of the weddings. How many weddings were not performed by notaries public?
Number of weddings not performed by notaries public
= (1 -0.17)*13249 ≈ 10997
A) 1099
B) 10994
C) 10997

14. State whether the statements are true or false:
A) True
B) False

15. Evaluate the expression:

3*5! = 3*5*4*3*2*1 = 360
A) 360
B) 120
C) 15

16. State whether the statements are true or false:
A) True
B) False

17. Fill in the missing value. Assume simple interest.
principal ________
interest rate 3%
time 1 year
simple interest $2,472.57
P = I/rt = 2472.57/(0.03*1) = 82419
A) principal $82,419
B) principal $85,419
C) principal $822,419

18. Determine whether the events A and B are independent

P(A ∩ B) ≠ P(A)*P(B), so events A and B are not independent.
A) Independent
B) Not Independent

19. If A and B are independent events, P(A)=.4, and P(B)=.6 find
P(A ∩ B) = P(A)*P(B) = 0.4*0.6 = 0.24
A) 0.24
B) 0.024
C) 0.0024

20. Find the probability. Write your answer as a fraction in simplest form:
You roll a number cube numbered from 1 to 6. P(1).
P(1) = n(E)/n(S) = 1/6
A) 1/6
B) 6
C) 1/3

21. A jar contains 25 green, 19 white, 6 pink, and 21 orange marbles. A marble is drawn at random. P(white, green, or pink)Express the probability as a fraction.
P(white, green, or pink) = n(E)/n(S) = (25+19+6)/71 = 50/71
A) 50/71
B) 71/50
C) 5/7

22. Fill in the missing value. Assume simple interest.
principal               $400,007
interest rate                  13%
time                    2 years
simple interest     ________
I = Prt = 400007*0.13*2 = $104001.82
A) simple interest $105,001.82
B) simple interest $104,001.82
C) simple interest $104,003.82

23. Find the probability. Write your answer as a percent rounded to the nearest whole percent:
A number from 8 to 16 is drawn at random. P(12).
P(12) = 1/9 = 0.11
A) 11%
B) 13%
C) 15%

24. Find the probability:
A number from 10 to 22 is drawn at random. P(an odd number) Express the probability as a decimal. Round to the nearest hundredth.
P(an odd number) = 6/13 = 0.46
A) 0.46
B) 0.17
C) 0.75

25. Determine whether the events A and B are independent

P(A ∩ B) = P(A)*P(B), so events A and B are independent.
A) Independent
B) Not Independent

26. Fill in the missing value. Assume simple interest.
principal               $87,698
interest rate                  ________
time                    1 year
simple interest     $6,138.86
r = I/pt = 6,138.86/(87,698*1) = 0.07
that is 7%
A) interest rate 7%
B) interest rate 8%
C) interest rate 10%

27. Let A and B be two events in a sample space S such that:

P(A | B) = P(A ∩ B)/P(B) = 0.2/0.5 = 2/5
A) 2/5
B) 5/2

28. A jar contains 21 pink and 26 navy marbles. A marble is drawn at random. P(navy)Express the probability as a decimal. Round to the nearest hundredth.
P(navy) = n(E)/n(S) = 26/47 = 0.55
A) 0.55
B) 0.055
C) 0.0055

29. Evaluate the expression: 9!
9! = 9*8*7*6*5*4*3*2*1 = 362880
A) 362880
B) 362800

30. A number from 15 to 26 is drawn at random. P(24)Express the probability as a percent. Round to the nearest percent.
P(24) = n(E)/n(S) = 1/12 = 0.08
A) 8%
B) 9%
C) 10%