Download MULTIPLE CHOICE. Choose the one alternative that best completes

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
A computer password consists of any five capital letters from the ordinary English alphabet (A through Z).
1) How many different passwords are possible? 1) __B_____
A) 26 × 5
B)
C) 26 × 25 × 24 × 23 × 22
D) 25
E) none of these
2) How many different passwords have no repeated letters?
2) ___C____
A)
B) 25
C) 26 × 25 × 24 × 23 × 22
D) 26 × 5
E) none of these
3) How many different passwords start with the letter Z?
3) ____A___
A)
B) 26 × 25
C)
D)
-1
E) none of these
A computer password is made up of five characters. Each character can be a capital letter (A through Z) or a digit (0
through 9).
4) How many passwords start with a digit?
4) __A_____
A) 10 ×
B)
C) 10 ×
D) 10 ×
E) none of these
A French restaurant offers a menu consisting of 5 different appetizers, 3 different salads, 2 different soups, 7 different
main courses, and 3 different desserts. The restaurant offers different combinations of "fixed price dinners" on
different days of the week.
5) On Monday through Thursday, the "fixed price dinner" consists of a choice of appetizer, a soup, a main course, and a
dessert. Assuming you don't pass on any of these, how many different "fixed price dinners" are possible on these days?
5) ___C____
A) 17
B) 70
C) 210
D) 42
E) none of these
6) On Fridays and Saturdays, the "fixed price dinner" consists of a choice of appetizer, a choice of either soup or salad, a
main course, and a dessert. Assuming you don't pass on any of these, how many different "fixed price dinners" are
possible on Fridays and Saturdays?
6) ___C____
A) 21
B) 630
C) 525
D) 20
E) none of these
7) On Sundays, the "fixed price dinner" consists of a main course, a dessert, and any two of the other three types of items
(i.e., appetizer and soup, or appetizer and salad, or soup and salad). Assuming you don't pass on any of these, how many
"fixed price dinners" are possible on Sundays? 7) ___C____
A) 5880
B) 420
C) 651
D) 30
E) none of these
Solve the problem.
8)
=
8) __B_____
A) 512
B) 336
C) 6720
D) 56
E) none of these
9)
=
9) _D______
A) 6720
B) 26
C) 336
D) 56
E) none of these
10)
=
10) ___B___
A)
B) 10!
C)
D) 1
E) none of these
11)
= 11) ___A___
A) 1
B) 100!
C) 100
D) 0
E) none of these
12)
+
A) 760,320
12) ___D___
B) 924 C) 12 D) 1716 E) 792
=
13)
A)
14)
A)
B)
13) ___D___
C) 500 D)
=
B) 500 C)
E) 501
14) ___D___
D)
E) 501
15) A music CD consists of 10 songs numbered 1 through 10. In how many ways can the 10 songs be ordered by the
random function on a CD player?
15) __A____
A) 10!
B)
C)
D) 10
E) none of these
16) A coin is tossed twice. The sample space for this random experiment is
A) {H, H, T, T}.
B) {HH, HT, TH, TT}.
C) {H, T}.
D) {HH, HT, TT}.
E) none of these
16) __B____
17) A fair coin is tossed three times. Which of the following describes the sample space for this random experiment?
17) __C____
A) {3 H's, 2 H's and 1 T, 1 H and 2 T's, 3 T's}
B) {H, T}
C) {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
D) {HHH, TTT}
E) none of these
A pair of honest dice is rolled, and the number on each die is noted.
18) Which of the following [A), B), C), or D)] is not an outcome in the sample space?
A) (5,2)
B) (6,6)
C) (4,5)
D) (1,1)
E) all of these are outcomes in the sample space.
19) How many different outcomes are there in the sample space? 19) ___E___
A) 12
B) 6
18) __E____
C) 30
D) 64
E) none of these
Solve the problem.
20) In the game of Yahtzee, a set of five dice is rolled at once, and the number on each die is observed. What is the size N
of the sample space?
20) ___A___
A)
B) 6!
C)
D)
E) none of these
21) A fair coin is tossed 6 times and heads or tails is noted on each toss. How many different outcomes are there in the
sample space? 21) __B____
A) 36
B) 64
C) 12
D) 2
E) none of these
22) A person shoots ten consecutive free throws and on each toss we observe either a success or a failure. How many
different outcomes are there in the sample space?
22) __A____
A)
B) 10
C) 20
D)
E) none of these
23) A person shoots ten consecutive free throws and the total number of successes is observed. How many different
outcomes are there in the sample space? 23) __A____
A) 11
B)
C) 5
D)
E) none of these
Four basketball teams called A, B, C, and D are entered in a tournament. According to the odds makers, the
probability that team A will win the tournament is Pr(A) = 0.1, and the other three teams all have an equal probability
of winning the tournament.
24) What is the probability that team A will not win the tournament?
24) __C____
A) 0.4
B) 0.3
C) 0.9
D) cannot be determined from the information given
E) none of these
25) What is the probability that team D will win the tournament? 25) ___D___
A) 0.25
B) 0.45
C) 0.9
D) 0.3
E) none of these
Solve the problem.
26) A pair of six-sided dice are rolled. The observation is the number that comes up on each die. The event described by
E: "both dice will come up as even numbers" is 26) ___B___
A) {(2, 4), (2, 6), (4, 2), (4, 6), (6, 2), (6, 4)}.
B) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}.
C) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4),
4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.
D) {(1, 1), (2, 2), (2, 4), (2, 6), (3, 3), (4, 2), (4, 4), (4, 6), (5, 5), (6, 2), (6, 4), (6, 6)}.
E) none of these
(4, 6), (5, 2), (5,
27) A pair of six-sided dice are rolled. The observation is the number that comes up on each die. The event described by
E: "at least one die will come up as an even number" is 27) ___A___
A) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4),
4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}.
(4, 6), (5, 2), (5,
B) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6),
1), (6, 2), (6, 3), (6, 4), (6, 5)}.
C) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}.
(5, 4), (5, 6), (6,
D) {(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1),
E) none of these
(6, 5)}.
28) A pair of six-sided dice are rolled. The observation is the number that comes up on each die. The event described by
E: "both dice come up with the same parity" (i.e., both numbers rolled are even or both numbers rolled are odd) is 28)
__C____
A) {(1, 3), (1, 5), (2, 4), (2, 6), (3, 1), (3, 5), (4, 2), (4, 6), (5, 1), (5, 3), (6, 2), (6, 4)}.
B) {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}.
C) {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2),
D) {(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}.
E) none of these
(6, 6)}.
29) A pair of six-sided dice are rolled. The observation is the number that comes up on each die. The event described by
E: "the sum of the two numbers rolled is 2, 4, or 6" is
29) __A____
A) {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (5, 1)}.
B) {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (5, 1), (6, 2)}.
C) {(1, 3), (1, 5), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (5, 1)}.
D) {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2)}.
E) none of these
A pitching machine throws 70% strikes and 30% balls. Five pitches will be thrown by the machine.
30) What is the probability that the machine will throw five balls?
30) __C____
A)
× 0.7
B)
C)
D) 0.3 + 0.3 + 0.3 + 0.3 + 0.3
E) none of these
1) B
2) C
3) A
4) A
5) C
6) C
7) C
8) B
9) D
10) B
11) A
12) D
13) D
14) D
15) A
16) B
17) C
18) E
19) E
20) A
21) B
22) A
23) A
24) C
25) D
26) B
27) A
28) C
29) A
30) C