MGF 1106 Exam #2
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a truth table to determine whether the two statements are equivalent.
1) q → p and ~q ∨ p
A) Yes
1)
B) No
Write the equivalent contrapositive of the statement.
2) If the TV is broken, then I cannot watch my programs.
A) If the TV is not broken, then I cannot watch my programs.
B) If I cannot watch my programs, then the TV is broken.
C) If the TV is not broken, then I can watch my programs.
D) If I can watch my programs, then the TV is not broken.
2)
Write the nonequivalent converse and inverse of the statement.
3) If you are getting a haircut, then you are not studying.
A) converse: If you are not getting a haircut, then you are studying
inverse: If you are not studying, then you are getting a haircut.
B) converse: If you are not studying, then you are getting a haircut.
inverse: If you are not getting a haircut, then you are studying
C) converse: If you are not studying, then you are getting a haircut.
inverse: If you are getting a haircut, then you are not studying
D) converse: If you are studying, then you are not getting a haircut.
inverse: If you are not getting a haircut, then you are studying
3)
Construct a truth table for the statement.
4) ~(p ∧ q) → ~(p ∨ q)
4)
A) p
q
~(p ∧ q) → ~(p ∨ q)
B) p
q
~(p ∧ q) → ~(p ∨ q)
T
T
F
F
C) p
T
F
T
F
q
F
T
T
T
~(p ∧ q) → ~(p ∨ q)
T
T
F
F
D) p
T
F
T
F
q
F
F
F
T
~(p ∧ q) → ~(p ∨ q)
T
T
F
F
T
F
T
F
T
T
F
F
T
F
T
F
T
T
T
T
T
F
F
T
Use a truth table to determine whether the symbolic form of the argument is valid or invalid.
5) p → q
~p
∴ ~q
A) Valid
B) Invalid
A‐1
5)
6) ~q ∧ ~p
p ∨ ~q
6)
∴ ~q
A) Valid
B) Invalid
Use an Euler diagram to determine whether the argument is valid or invalid.
7) All dogs are animals.
Some animals are pets.
Therefore, some dogs are pets.
A) valid
7)
B) invalid
8) All wrestlers are strong.
Some wrestlers are smart.
8)
Therefore, some strong people are smart.
A) valid
B) invalid
9) Some cars are considered sporty.
Some cars are safe at high speeds.
Therefore, Some sports cars are safe at high speeds.
A) valid
9)
B) invalid
Solve the problem by applying the Fundamental Counting Principle with two groups of items.
10) An apartment complex offers apartments with four different options, designated by A through D.
10)
A = number of bedrooms (one through four)
B = number of bathrooms (one through three)
C = floor (first through fifth)
D = outdoor additions (balcony or no balcony)
How many apartment options are available?
A) 120
B) 240
C) 14
D) 16
Use the formula for nPr to solve.
11) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are
possible if there are 15 members and any member can be elected to each position? No person can
hold more than one office.
A) 32,760
B) 1365
C) 2730
D) 910
11)
Use the formula for nCr to evaluate the expression.
12) In how many ways can a committee of three men and four women be formed from a group of 11
men and 11 women?
A) 554,400
B) 110
C) 7,840,800
D) 54,450
A‐2
12)
Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest
terms.
13)
13) Use the spinner below to answer the question. Assume that it is equally probable
that the pointer will land on any one of the five numbered spaces. If the pointer lands
on a borderline, spin again.
Find the probability that the arrow will land on an odd number.
3
A) 0
B)
C) 1
5
D)
2
5
Solve the problem.
14) Six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is determined
by random selection. Find the probability that (a) E will speak first (b) that C will speak fifth and B
will speak last (c) that the students will speak in the following order: DECABF (d) that A or B will
speak first.
1 1
1 1
1 1
1 1
1
1
1 1
1 1
1 1
; B) ; ; ; C) ; ; ; D) ; ; ; A) ; ; 6 36 360 3
6 36 720 12
6 12 720 3
6 24 720 3
15) A committee consisting of 6 people is to be selected from eight parents and four teachers. Find the
probability of selecting three parents and three teachers.
10
8
100
2
B)
C)
D)
A)
11
33
231
33
14)
15)
The chart shows the probability of a certain disease for men by age. Use the information to solve the problem. Express
all probabilities as decimals, estimated to two decimal places.
Age
20-24
25-34
35-44
45-54
55-64
65-74
75+
Probability of Disease X
less than 0.008
0.009
0.14
0.39
0.42
0.67
0.79
16) What is the probability that a randomly selected man between the ages of 55 and 64 does not have
this disease?
A) 0.39
B) 0.61
C) 0.58
D) 0.42
16)
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3),
(2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,
6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}.
17)
17) Find the probability of getting a sum of 4 or 5.
1
2
1
7
B)
C)
D)
A)
9
9
12
36
A‐3
Solve the problem that involves probabilities with events that are not mutually exclusive.
18) In a class of 50 students, 23 are Democrats, 9 are business majors, and 7 of the business majors are
Democrats. If one student is randomly selected from the class, find the probability of choosing a
Democrat or a business major.
1
16
39
1
B)
C)
D)
A)
2
25
50
25
Solve the problem involving probabilities with independent events.
19) If you toss a fair coin 11 times, what is the probability of getting all heads?
1
1
1
A)
B)
C)
4096
1024
2
18)
19)
1
D)
2048
The table shows the number of minority officers in the U.S. military in 2000.
African Americans
Hispanic Americans
Other Minorities
Army
9162
2105
4075
Navy
3524
2732
2653
Marines
1341
914
599
Air Force
4282
1518
3823
Assume that one person will be randomly selected from the group described in the table.
20) Find the probability of selecting an officer who is in the Navy, given that the officer is African
American.
8909
3524
3524
3542
B)
C)
D)
A)
18,309
18,309
8909
14785
A‐4
20)
Answer Key
Testname: EXAM2
1) A
2) D
3) B
4) D
5) B
6) A
7) B
8) A
9) B
10) A
11) C
12) D
13) B
14) A
15) C
16) C
17) A
18) A
19) D
20) C
A‐5
MGF 1106 Exam #2
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