Download Chapter 4 - Practice Problems 2

Chapter 4 - Practice Problems 2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the indicated probability.
1) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT.
What is the probability of getting at least one head?
A)
3
4
B)
7
8
C)
1
2
D)
1
4
2) If two balanced die are rolled, what is the probability that the sum of the dice is 4 or 12.
A)
1
9
B)
1
12
C)
5
36
D)
C)
1
2
D)
2)
1
6
3) A committee of three people is to be formed. The three people will be selected from a list of five
possible committee members. A simple random sample of three people is taken, without
replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five
people, list the possible samples of size three and use your list to determine the probability that B
is included in the sample. (Hint: There are 10 possible samples. List them all)
2
3
B)
A)
5
5
1)
3)
7
10
4) A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip
is selected at random from the bag and then replaced in the bag. A second chip is then selected at
random. Make a list of the possible outcomes (for example RB represents the outcome red chip
followed by blue chip) and use your list to determine the probability that the two chips selected
are the same color.
4)
(Hint: There are 16 possible outcomes.)
A)
1
8
B)
1
2
C)
1
4
D)
1
16
Estimate the probability of the event.
5) The data set represents the income levels of the members of a country club. Estimate the
probability that a randomly selected member earns at least $100,000. Round your answers to the
nearest tenth.
112,000 124,000 92,000 130,000 96,000 112,000 100,000 84,000 142,000 172,000 88,000 106,000 136,000
96,000 124,000 118,000 100,000 148,000 80,000 118,000
A) 0.6
B) 0.7
C) 0.4
1
D) 0.8
5)
List the outcomes comprising the specified event.
6) When a quarter is tossed four times, 16 outcomes are possible.
HHHH
HTHH
THHH
TTHH
HHHT
HTHT
THHT
TTHT
HHTH
HTTH
THTH
TTTH
6)
HHTT
HTTT
THTT
TTTT
Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are
tails, and the fourth toss is heads. List the outcomes that comprise the following event.
A = event exactly three tails are tossed
A) HTTT, THTT, TTHT, TTTH, TTTT
C) HTTT, THTT, TTHT, TTTH
B) TTTH
D) HTTT, THTT, TTTH
7) Three board members for a nonprofit organization will be selected from a group of five people.
The board members will be selected by drawing names from a hat. The names of the five possible
board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be
represented as follows.
ABC
ADE
ABD
BCD
ABE
BCE
ACD
BDE
7)
ACE
CDE
Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be
on the board. List the outcomes that comprise the following event.
A = event that fewer than two men are selected
A) ABC, ABD, ADE, BCE, BDE
C) ABC, ABD, ABE, ACE, ADE, BCE, BDE
B) ABC, ABD, ACE, ADE, BCE, BDE
D) ACD, BCD, CDE
Describe the specified event in words.
8) When a quarter is tossed four times, 16 outcomes are possible.
The events A and B are defined as follows.
A = event exactly two tails are tossed
B = event the first toss is heads
Describe the event (A or B) in words.
A) Event that the first toss is heads or the last two tosses are tails or both
B) Event that exactly two tails are tossed and the first toss is heads
C) Event that exactly two tails are tossed or the first toss is heads but not both
D) Event that exactly two tails are tossed or the first toss is heads or both
2
8)
9) The age distribution of students at a community college is given below.
Number of students (f)
Age (years)
Under 21
4946
21 -25
4808
26 -30
2673
31 -35
2036
Over 35
525
9)
A student from the community college is selected at random. The event A is defined as follows.
A = event the student is between 26 and 35 inclusive.
Describe the event (not A) in words.
A) The event the student is at most 26 or at least 35
B) The event the student is under 26 or over 35
C) The event the student is under 26 and over 35
D) The event the student is over 35
Determine the number of outcomes that comprise the specified event.
10) The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21
2170
21-25
2197
26-30
1190
31-35
855
Over 35
205
10)
A student from the community college is selected at random. The event A is defined as follows.
A = event the student is between 26 and 35 inclusive.
Determine the number of outcomes that comprise the event (not A).
A) 5427
B) 4367
C) 4572
3
D) 2045
11) The number of hours needed by sixth grade students to complete a research project was recorded
with the following results.
Number of students (f)
Hours
4
26
5
27
6
15
7
14
8
13
9
4
10+
6
11)
A student is selected at random. The events A and B are defined as follows.
A = the event the student took between 6 and
9 hours inclusive
B = the event the student took at most 7 hours
Determine the number of outcomes that comprise the event (A or B).
A) 46
B) 128
C) 29
D) 99
Determine whether the events are mutually exclusive.
12) The number of hours needed by sixth grade students to complete a research project was recorded
with the following results.
Number of students (f)
Hours
4
15
5
11
6
19
7
6
8
9
9
16
10+
2
A student is selected at random. The events A, B, and C are defined as follows.
A = event the student took more than 9 hours
B = event the student took less than 6 hours
C = event the student took between 7 and
9 hours inclusive
Is the collection of events A, B, and C mutually exclusive?
A) Yes
B) No
4
12)
Find the indicated probability.
13) A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly
selected from the bag, what is the probability that it is blue?
A)
1
3
B)
1
5
C)
3
14
D)
1
6
14) A class consists of 59 women and 62 men. If a student is randomly selected, what is the probability
that the student is a woman?
A)
59
62
B)
59
121
C)
62
121
D)
13)
14)
1
121
Find the indicated probability by using the special addition rule.
15) A relative frequency distribution is given below for the size of families in one U.S. city.
Relative frequency
Size
2
0.399
3
0.247
4
0.210
5
0.096
6
0.029
7+
0.019
15)
A family is selected at random. Find the probability that the size of the family is less than 5. Round
approximations to three decimal places.
A) 0.553
B) 0.096
C) 0.856
D) 0.457
16) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face
card or a 5?
48
2
4
C)
D)
A) 16
B)
52
13
13
16)
17) Two 6-sided dice are rolled. What is the probability that the sum of the numbers on the dice is 6 or
9?
3
5
1
1
B)
C)
D)
A)
2
12
4
54
17)
Find the indicated probability by using the complementation rule.
18) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore
leap years.
A)
334
365
B)
31
365
C)
5
11
12
D)
31
334
18)
19) The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21
409
21-24
404
25-28
276
29-32
155
33-36
97
37-40
63
Over 40
86
19)
1490
A student from the community college is selected at random. Find the probability that the student
is 21 years or over. Give your answer as a decimal rounded to three decimal places.
A) 0.295
B) 0.271
C) 0.274
D) 0.726
Find the indicated probability.
20) The following contingency table provides a joint frequency distribution for the popular votes cast
in the presidential election by region and political party. Data are in thousands, rounded to the
nearest thousand.
A person who voted in the presidential election is selected at random. Compute the probability
that the person selected voted Democrat.
A) 0.442
B) 0.098
C) 0.406
6
D) 0.241
20)
21) The table below shows the soft drink preferences of people in three age groups.
under 21 years of age
between 21 and 40
over 40 years of age
cola root beer lemon-lime
40
25
20
35
20
30
20
30
35
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and
drinks cola.
4
17
A)
4
51
B)
C)
4
19
D) None of the above is correct.
7
21)
Answer Key
Testname: CH 4 SET 2
1) B
2) A
3) A
4) C
5) B
6) C
7) C
8) D
9) B
10) C
11) D
12) A
13) C
14) B
15) C
16) B
17) D
18) A
19) D
20) C
21) A
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