Finite Practice Exam

Exam 1 - Version 1
This is a 50 minute test.

1. Of a group of 100 people, 33 like earrings, 29 like tattoos, and 26 like tattoos but don't like earrings. How many like neither earrings nor tattoos?
(A) 59

(B) 41

(C) 38

(0) 12 (E) none of the others

2. In the diagram belovv,which of the following is true?

C.

I

(A) x E (A n G') U (B n G)
(0) x E (A n G) U (B' n G)

(B) x E (A U B) n (A' U G)
(E) none of the others

n G') n (B n G)

(C) x E (A

3. Two 6-sided dice are rolled. What is the probability that at least one of the dice shows a I?
(A) 1/3

(B) 1/12

(C) 11/36

(D) 1/6

(E) none of the others

4. A saleswoman is scheduling trips to visit 3 of the following 6 cities: Cleveland, Chicago, St.
Louis, Buffalo, Detroit, and Kansas City. A schedule is a list of the 3 cities in the order to be visited. How many different schedules are there which include Kansas City?
(A) 60

(B) 120

(C) 20

(0) 24 (E) none of the others
,

5. Find n (A n B), given that A and B are subsets of U with n (A) = 31, and n (B') = 10.
(A) 29

(B) 44

(C) 21

(D) 33

n (U) =

52,

n (A' n

B')

=

8,

(E) none of the others

6. A Greek urn contains a red ball, a blue ball, a yellow ball, and an orange ball. A ball is drawn from the urn at random and then replaced. If one does this 4 times, what is the probability that all 4 colors were selected?
(A) 1/70

(B) 3/32

(C) 2/9

(D) 1/4

(E) none of the others

7. A fortune teller foretells that each of 4 boys (Eric, Jason, Jeff, Kevin) will marry one of 4 girls
(Jodie, Lisa, Susan, Wendy). How many ways can this be done? (No divorces or bigamy please!)
(A) 12

(B) 6

(C) 44

(D) 24

7

(E) none of the others

Exam 1 - \ersi on 1
8. How many 4-letter words can be formed by rearranging the letters in the word "seek"?
(A) 12

(B) 24

(C) 6

(0) 24

(E) none ofthe others

9. Godzilla wants to destroy two buildings: a fast-food