MATH 17 PRACTICE Final Exam B

These questions were written by students in MATH 17 based on the homework assignments. Since no one has had access to the exam that will be given, these questions may not be an accurate representation of the actual exam questions.

1. Which of the following is a proposition?

a. Did you study for the exam?

b. There are exactly 30 questions on the test.

c. I forgot to study!

d. Where is the exam being held?

2. Let p denote ”Meghan studied for the test” and q denote “Mike studied for the test”. Which of the following denotes “neither Meghan nor Mike studied for the test”?

a. ~p ^ q

b. ~(p v q)

c. ~(p ^ q)

d. p ^ ~ q

3. ~p ^ ~q is logically equivalent to

a. p v q

b. ~(p ^ q)

c. ~(p v q)

d. p ^ q

p	q	(p v ~q) ^ p
T	T
T	F	x
F	T	y
F	F

a. x = T and y = F

b. x = T and y = T

c. x = F and y = T

d. x = F and y = F

5. Which of the following conclusions would be true given these implications?

a. b

6. is logically equivalent to

c. ^

7. Given the following propositions: If I do not paint the house, I will go bowling. I will not go bowling.

A valid conclusion is

a. I will paint the house.

b. I will not paint the house.

c. I will go bowling.

d. The house does not need painting.

8. Hypotheses: When students study, they receive good grades.

These students do not study.

Conclusion: These students do not receive good grades.

This argument is

a. Valid.

b. Invalid.

c. Bogus.

d. Impossible.

9. If A = {1, 3, 5, 7, 9, 11} and Z = {3, 4, 5, 6, 7, 13, 15}, then A Z =

a. {3, 5, 7}

c. {1, 3, 4, 5, 6, 7, 9, 11, 13, 15}

d. {1, 4, 6, 9, 11, 13, 15}

10. If U = { q, r, s, t, u, v} and A = {q, r, s}, then =

a. { }

b. {q, r, s}

c. {t, u, v}

d. {q, r, s, t, u, v}

11. Given A = {0, 1, 2, 3} and B = {2, 3, 4}, then c(A U B) =

a. 5

b. 9

c. 2

d. 7

12. Given c(A) = 5, c(B) = 4 and c(A U B) = 7, then c(A B) =

a. 11

b. 2

c. 9

d. 16

13. How many PSU access ID’s are possible if each ID consists of 3 letters followed be exactly 4 digits? Letters and digits can be repeated.

a. 26 x 25 x 24 x 10⁴

b. 26 x 25 x 24 x 10 x 9 x 8 x 7

c. 26³x 10⁴

d. 26³ x 10 x 9 x8 x 7 x 6

14. You are going on a trip to your grandma’s house. Driving down the road, you come to a four-way stop. Each of the roads at the stop eventually fork into two separate roads each. These separate roads then all pointlessly converge on your grandma’s home. How many different routes can you take to get there?

a. 6

b. 3

c. 2

d. 5

15. How many 3-letter codes can be formed using any letter of the alphabet except A, B, and C? Also, none of the letters can be repeated.

a. 250

b. 1,150

c. 2,500

d. 10,626

16. How many ways can 6 students be lined up against a fence?

a. 200

b. 720

c. 20

d. 450

17. What is C(5,3)?

a. 5

b. 2

c. 3

d. 10

18. In how many ways can a committee of 4 executives be formed from a pool of 7 executives?

a. P(4, 7)

b. C(7, 4)

c. C(4, 7)

d. P(7, 4)

19. How many subsets with an even number of elements does a set with 5 elements have?

a. 10

b. 32

c. 16

d. 64

20. The coefficient of x²y⁴in the expansion of (x +y)⁶ is

a. 20

b. 15

c. 10

d. 6

21. A coin is flipped 5 times. The number of outcomes in the sample space is

a. 5

b. 10

c. 5²

d. 2⁵

22. A fair pair of dice is tossed. What is the probability that a sum of 5 or 8 is tossed?

a. 1/6

b. 2/9

c. 13/36

d. 1/18

23. If P(A) = .35 , P(B) = .40 and A and B are mutually exclusive. P(A U B) =

a. .75

b. .25

c. .15

d. .35

24. Suppose the probability of event E is .3. The odds against event E is

a. 7 to 3

b. 7 to 1

c. 3 to 10

d. 3 to 7

25. A box contains 8 bulbs and 3 of them are defective. All bulbs look alike and have an equal chance of being chosen. 2 light bulbs are selected and placed in a box. The probability that both bulbs are defective is

a. ¼

b. 3/28

c. 1/14

d. 3/8

26. A fair coin is tossed 4 times. The probability of tossing exactly 3 or 4 heads is

a. ¼

b. 1/16

c. 5/16

d. 15/16

27. Given P(E) = .2, P(F) = .3, and P(E F) = .1.

a. 6/7

b. 8/7

c. 1/7

d. 4/7

28. A card is drawn at random from a regular deck of 52 cards. The probability that the card is a red queen is

a. 2/52

b. 1/52

c. 26/52

d. 13/52

29. Assume events A and B are independent. If P(A) = .2 and P(B) = .9, then P(A B) =

a. .11

b. .18

c. .7

d. 0

30. People were surveyed for the color of their hair and the results are presented in the table.

	Brown Hair (B)	Not Brown Hair ()	Totals
Female (F)	15	6	21
Male ()	9	3	12
Totals	24	9	33

a. P(B|F) = 5/7 and B and F are independent events.

b. P(B|F) = 5/7 and B and F are not independent events.

c. P(B|F) = 8/11 and B and F are independent events.

d. P(B|F) = 8/11 and B and F are not independent events.