MATH 17 PRACTICE Final Exam A

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. Let p denote “John likes reading” and let q denote “Adam likes to swim”. The symbolic representation for “John doesn’t like reading and Adam likes to swim.” is

a. ~(p v q)

b. ~p v ~q

c. p ^ q

d. ~p ^ q

2. The negation of the proposition “I have been to all classes.” Is

a. I have not been to some classes.

b. We have been to every class.

c. I have not been to any classes.

d. I have been to some classes.

3. Which of the following statements is an example of the commutative property?

a. p ^ q q ^ p

b. (p ^ q) ^ r p ^ (q ^ r)

c. p v (q ^ r) (p v q ) ^ (p v r)

d. p ^ p p

4.

p	q	~q	p v ~q
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. Let p denote “The examination is hard” and let q denote “the grades are low”. The symbolic representation for “If the examination is hard, the grades are not low.” Is

a.

b. ~

c.

d.

6. The converse of the statement ~ is

a.

b.

c. ~

d. ~

7. Hypotheses: If Smith is elected president, then Kuntz will be elected secretary.

If Kuntz is elected secretary, then Brown will not be elected treasurer.

Smith is elected president.

Conclusion: Brown is not elected treasurer

To prove that this is a valid argument by using the indirect proof method, you would begin by assuming that

a. Brown is elected treasurer.

b. Brown is not elected treasurer.

c. Smith is elected president.

d. Smith is not elected president.

8. Given is true and is true, then concluding that is true is an example of the

a. Law of disjunction.

b. Law of contrapositive.

c. Law of syllogism.

d. Law of detachment.

9. If U = Universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9}and if A = {0, 1, 5, 7}, B = {2, 3, 5, 8} and C = {5, 6, 9}, then

a. {0, 1, 6, 8}

b. {1, 5, 7}

c. {0, 1, 5, 7}

d. {2, 3, 7}

10. Let U = {a, b, c, d, e, f}, A = {b, c} and B = {c, d, e}. the elements of is

a. {a, f}

b. {b, c, d, e}

c. {c}

d. {a, b, d, e, f}

11. Find , given c(A) = 28, c(B) = 22 and = 6.

a. 44

b. 56

c. 12

d. 0

U

12.

A B

10 6 8

3

5 2

20 5

C

How many elements are in the set ?

a. 30

b. 49

c. 35

d. 24

13. A man has 3 pairs of shoes, 8 pairs of socks, 4 pairs of slacks and 9 sweaters. How many different outfits can he choose to wear?

a. 24

b. 864

c.

d. None of the above.

14. How many license plates consisting of 2 letters (uppercase) followed by 2 digits are possible? Repetition of letters and digits are allowed.

a. 26 + 26 + 10 + 10

b. 26 x 25 x 10 x 9

c. 26² x 10 x 9

d. 26 x 26 x 10 x 10

15. In how many ways can 4 people be lined up?

a. C(4,4)

b. 4!

c. P(4, 1)

d. 4

16. In how many different ways can 2 people each have different birthdays? (Assume 365 days in a year.)

a. C(365, 2)

b. 365!

c. P(365, 2)

d.

17. How many different 9 letter word (real or imaginary ) can be formed from the letters in the word ECONOMICS?

a. 9

b. 9!

c.

d.

18. In the U.S. Congress a committee is to be composed of 5 senators and 4 representatives. In how many ways can this be done? (There are 435 representatives and 100 senators.)

a. P(435, 4) x P(100, 5)

b. P(435, 4) + P(100, 5)

c. C(435, 4) x C(100, 5)

d. C(435, 4) + C(100, 5)

19. What is the coefficient of x⁸ in the expression (x + 3)¹⁰ ?

a.

b.

c.

d. 5

20. Which of the following expressions is not equal to C(6, 4)?

a.

b.

c.

d.

21. A weighted coin is tossed and tails is 5 times more likely to occur than heads. A probability model for this experiment is

a. P(H) = 1 and P(T) = 5

b. P(H) = 1/5 and P(T) = 4/5

c. P(H) = 1/6 and P(T) = 5/6

d. P(H) = 1/7 and P(T) = 5/7

22. A bag contains 4 red balls, 3 green balls, 6 orange balls and 5 black balls. The probability that a black ball is drawn is

a. 5/18

b. 13/18

c. 1/18

d. 5/13

23. The P(A) = .36, P(B) = .52 and A and B are mutually exclusive. The

a. .36/0

b. 0.88

c. 0.16

d. 0.1872

24. Determine the probability of the event E for the given odds 8 to 6 for E.

a. 3/7

b. 4/3

c. 3

d. 4/7

25. What is the probability that in a group of 6 people, at least 2 were born in the same month? (Disregard day and year.)

a.

b.

c.

d.

26. Through a mix-up on the production line, 8 defective freezers were shipped out with 32 good ones. If 5 are selected at random, what is the probability that 3 are defective?

a.

b.

c. 3 x 32

d.

27. 100 females and 100 males were surveyed to determine their ice cream flavor preference. The results are presented in the table.

	Vanilla	Chocolate	Strawberry	Total
Female	32	60	8	100
Male	48	12	40	100
Total	80	72	48	200

The probability that a female prefers chocolate ice cream is

a. 60/200

b. 60/100

c. 72/200

d. 40/100

28. Two cards are drawn at random without replacement. What is the probability that the first card is a number card (1 - 10) and the second is a face card?

a.

b.

c.

d.

29. The casuality rate from DUI-related accidents is .4. Out of 5 individual drivers, what is the probability that all survive a DUI-related accident?

a. (.6)⁵

b. (.4)⁵

c. 1 - .6

d. .24

30. Jacob and Tye are playing Dungeons and Dragons. They are rolling a 12-sided die. Let E be the event that a 1, 2, 3, 4, 5, or 6 is rolled. Let F be the event that a 4, 7, 8, 9, 10, 11, or 12 is rolled. Are the events E and F independent?

a. Yes

b. No

c. Not enough information.

d. I missed the class on Independence.