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Math Problems
Algebra 2
Find probabilities using the addition rule
In a certain Algebra
2
2
2
class of
23
23
23
students,
6
6
6
of them play basketball and
10
10
10
of them play baseball. There are
11
11
11
students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
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Chen has an MP
3
3
3
player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has
4
4
4
classical songs,
3
3
3
rock songs, and
2
2
2
rap songs on it. Chen is going to listen to
360
360
360
songs.
\newline
What is the best prediction for the number of times Chen will listen to a classical song?
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly
90
90
90
times
\newline
(B) Close to
90
90
90
times but probably not exactly
90
90
90
times
\newline
(C) Exactly
160
160
160
times
\newline
(D) Close to
160
160
160
times but probably not exactly
160
160
160
times
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A survey was done of commuters in three major cities about how they primarily got to work. The results are shown in the frequency table below. Answer the following conditional probability questions to the nearest hundredth, if necessary.
\newline
a) What is the probability that a person picked at random would take a train to work given that they live in Los Angeles?
\newline
b) What is the probability that a person picked at random
\newline
\begin{array}{|c|c|c|c|} \hline & \text{Car} & \text{Train} & \text{Walk} & \text{Total} \ \hline \text{New York} & .05 & .25 & .10 & .40 \ \text{Los Angeles} & .18 & .12 & .05 & .35 \ \text{Chicago} & .08 & .14 & .03 & .25 \ \text{Total} & .31 & .51 & .18 & 1.00 \ \hline \end{array}
\newline
would live in New York given that they drive a car to work?
\newline
c) Is it more likely that a person who takes a train to work lives in Chicago or more likely that a person who lives in Chicago will take a train to work. Support your work using conditional probabilities.
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Find the number of distinguishable permutations of the given letters ＂AAABBBCD＂.
\newline
There are:
_
\_
_
permutations.
\newline
If a permutation is chosen at random, what is the probability that it begins with at least
2
2
2
A's?
\newline
The probability is
_
\_
_
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Question
8
8
8
,
3
3
3
.
2
2
2
.
19
19
19
\newline
HW Score:
\newline
36.46
%
36.46\%
36.46%
,
5.83
5.83
5.83
of
16
16
16
points
\newline
Part
2
2
2
of
5
5
5
\newline
Points:
0
0
0
of
1
1
1
\newline
The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a ＂flipped＂ classroom. Complete parts (a) through (c) below.
\newline
\newline
Traditional
\newline
71.1
71.1
71.1
\newline
80.5
80.5
80.5
\newline
79.9
79.9
79.9
\newline
67.8
67.8
67.8
\newline
84.3
84.3
84.3
\newline
5.83
5.83
5.83
0
0
0
\newline
5.83
5.83
5.83
1
1
1
\newline
\newline
80.5
80.5
80.5
\newline
5.83
5.83
5.83
3
3
3
\newline
5.83
5.83
5.83
4
4
4
\newline
5.83
5.83
5.83
5
5
5
\newline
5.83
5.83
5.83
6
6
6
\newline
5.83
5.83
5.83
7
7
7
\newline
\newline
Flipped
\newline
5.83
5.83
5.83
8
8
8
\newline
5.83
5.83
5.83
9
9
9
\newline
16
16
16
0
0
0
\newline
16
16
16
1
1
1
\newline
16
16
16
2
2
2
\newline
16
16
16
3
3
3
\newline
16
16
16
4
4
4
\newline
\newline
16
16
16
2
2
2
\newline
16
16
16
6
6
6
\newline
16
16
16
7
7
7
\newline
16
16
16
8
8
8
\newline
16
16
16
9
9
9
\newline
0
0
0
0
0
0
\newline
\newline
(a) Which course has more dispersion in exam scores using the range as the measure of dispersion?
\newline
The traditional course has a range of
0
0
0
1
1
1
, while the ＂flipped＂ course has a range of
0
0
0
2
2
2
. The flipped course has more dispersion.
\newline
(Type integers or decimals, Do not round.)
\newline
(b) Which course has more dispersion in exam scores using the sample standard deviation as the measure of dispersion?
\newline
The traditional course has a standard deviation of
\newline
0
0
0
3
3
3
, while the ＂flipped＂ course has a standard deviation of
\newline
0
0
0
3
3
3
. The
\newline
0
0
0
3
3
3
course has more dispersion.
\newline
(Round to three decimal places as needed.)
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.12
0.12
0.12
and the probability that the flight will be delayed is
0.1
0.1
0.1
. The probability that it will not rain and the flight will leave on time is
0.8
0.8
0.8
. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
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This season, the probability that the Yankees will win a game is
0.48
0.48
0.48
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0.57
0.57
0.57
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0.31
0.31
0.31
. What is the probability that the Yankees will lose when they score fewer than
5
5
5
runs? Round your answer to the nearest thousandth.
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In a certain Algebra
2
2
2
class of
29
29
29
students,
6
6
6
of them play basketball and
19
19
19
of them play baseball. There are
6
6
6
students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
24
24
24
students,
13
13
13
of them play basketball and
5
5
5
of them play baseball. There are
8
8
8
students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
\newline
Answer:
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In a certain Algebra
2
2
2
class of
25
25
25
students,
5
5
5
of them play basketball and
14
14
14
of them play baseball. There are
8
8
8
students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
\newline
Answer:
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In a math class with
26
26
26
students, a test was given the same day that an assignment was due. There were
17
17
17
students who passed the test and
18
18
18
students who completed the assignment. There were
14
14
14
students who passed the test and also completed the assignment. What is the probability that a student chosen randomly from the class failed the test?
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
52
52
52
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
6
6
6
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
33
33
33
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
12
12
12
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
84
84
84
. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
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In a class of
24
24
24
students,
5
5
5
play an instrument and
15
15
15
play a sport. There are
6
6
6
students who do not play an instrument or a sport. What is the probability that a student plays an instrument given that they play a sport?
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
52
52
52
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
6
6
6
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
33
33
33
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
05
05
05
. The probability that it will rain and the flight will be delayed is
0
0
0
.
03
03
03
. What is the probability that it is raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
51
51
51
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
57
57
57
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
45
45
45
. What is the probability that the Yankees would score
5
5
5
or more runs when they lose the game? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
19
19
19
and the probability that the flight will be delayed is
0
0
0
.
17
17
17
. The probability that it will rain and the flight will be delayed is
0
0
0
.
05
05
05
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
52
52
52
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
56
56
56
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
4
4
4
. What is the probability that the Yankees would score fewer than
5
5
5
runs when they lose the game? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
61
61
61
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
43
43
43
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
36
36
36
. What is the probability that the Yankees will lose when they score fewer than
5
5
5
runs? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
06
06
06
and the probability that the flight will be delayed is
0
0
0
.
06
06
06
. The probability that it will rain and the flight will be delayed is
0
0
0
.
02
02
02
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
12
12
12
and the probability that the flight will be delayed is
0
0
0
.
15
15
15
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
83
83
83
. What is the probability that the flight would leave on time when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
12
12
12
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
84
84
84
. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
12
12
12
and the probability that the flight will be delayed is
0
0
0
.
1
1
1
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
81
81
81
. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
13
13
13
and the probability that the flight will be delayed is
0
0
0
.
1
1
1
. The probability that it will rain and the flight will be delayed is
0
0
0
.
05
05
05
. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
19
19
19
and the probability that the flight will be delayed is
0
0
0
.
08
08
08
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
78
78
78
. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
18
18
18
and the probability that the flight will be delayed is
0
0
0
.
08
08
08
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
81
81
81
. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
54
54
54
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
52
52
52
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
43
43
43
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
51
51
51
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
52
52
52
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
37
37
37
. What is the probability that the Yankees would score fewer than
5
5
5
runs when they win the game? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
19
19
19
and the probability that the flight will be delayed is
0
0
0
.
17
17
17
. The probability that it will rain and the flight will be delayed is
0
0
0
.
05
05
05
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
Submit Answer
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
12
12
12
and the probability that the flight will be delayed is
0
0
0
.
18
18
18
. The probability that it will rain and the flight will be delayed is
0
0
0
.
09
09
09
. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
62
62
62
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
54
54
54
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
45
45
45
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
16
16
16
and the probability that the flight will be delayed is
0
0
0
.
15
15
15
. The probability that it will rain and the flight will be delayed is
0
0
0
.
01
01
01
. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
54
54
54
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
51
51
51
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
38
38
38
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
48
48
48
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
57
57
57
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
37
37
37
. What is the probability that the Yankees win and score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
1
1
1
and the probability that the flight will be delayed is
0
0
0
.
18
18
18
. The probability that it will rain and the flight will be delayed is
0
0
0
.
02
02
02
. What is the probability that the flight would leave on time when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
15
15
15
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
8
8
8
. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
53
53
53
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
49
49
49
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
39
39
39
. What is the probability that the Yankees will win when they score fewer than
5
5
5
runs? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
09
09
09
and the probability that the flight will be delayed is
0
0
0
.
08
08
08
. The probability that it will rain and the flight will be delayed is
0
0
0
.
01
01
01
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
09
09
09
and the probability that the flight will be delayed is
0
0
0
.
07
07
07
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
86
86
86
. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
05
05
05
. The probability that it will rain and the flight will be delayed is
0
0
0
.
03
03
03
. What is the probability that it is raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
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120
120
120
students in a fifth grade class are surveyed about what kinds of pets they have. Of the
120
120
120
students,
30
30
30
have a goldfish,
40
40
40
have a mouse, and
10
10
10
have a goldfish and a mouse. Using this information, answer each of the following questions. Let
G
G
G
be the event that a randomly selected student has a goldfish and
M
M
M
be the event that a randomly selected student has a mouse.What is
P
(
G
)
P(G)
P
(
G
)
, the probability that a student in the class has a goldfish? What is
P
(
M
)
P(M)
P
(
M
)
, the probability that a student in the class has a mouse? What is
P
(
G
∩
M
)
P(G \cap M)
P
(
G
∩
M
)
, the probability that a student in the class has a goldfish and a mouse? What is
P
(
G
∪
M
)
P(G \cup M)
P
(
G
∪
M
)
, the probability that a student in the class has a goldfish or a mouse?
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You're a manager in a company that produces rocket ships. Machine
A
A
A
and Machine
B
B
B
both produce cockpits and propulsion systems. Machine
A
A
A
ran for
22
22
22
hours and produced
3
3
3
cockpits and
5
5
5
propulsion systems. Machine
B
B
B
ran for
44
44
44
hours and produced
6
6
6
cockpits and
10
10
10
propulsion systems.
\newline
Assume both machines produce cockpits at the same rate and both produce propulsion systems at the same rate.
\newline
Can we use a system of linear equations in two variables to solve for a unique amount of time that it takes each machine to produce a cockpit and to produce a propulsion system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; it takes Machine
A
A
A
and Machine
B
B
B
2
2
2
hours to produce a cockpit and
4
4
4
hours to produce a propulsion system.
\newline
(B) Yes; it takes Machine
A
A
A
and Machine
B
B
B
4
4
4
hours to produce a cockpit and
2
2
2
hours to produce a propulsion system.
\newline
(C) No; the system has many solutions.
\newline
(D) No; the system has no solution.
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Sophia has a bag with
3
3
3
purple marbles and
4
4
4
blue marbles in it. She is going to randomly draw a marble from the bag
280
280
280
times, putting the marble back in the bag after each draw.
\newline
Complete the following statement with the best prediction.
\newline
Sophia will draw a purple marble...
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly
120
120
120
times
\newline
(B) Close to
120
120
120
times but probably not exactly
120
120
120
times
\newline
(C) Exactly
160
160
160
times
\newline
(D) Close to
160
160
160
times but probably not exactly
160
160
160
times
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Pat's Pizza made
21
21
21
cheese pizzas,
14
14
14
veggie pizzas,
23
23
23
pepperoni pizzas, and
14
14
14
sausage pizzas yesterday.
\newline
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza? Choose the best answer. Choose
1
1
1
answer:
\newline
(A)
51
%
51 \%
51%
\newline
(B)
66
%
66 \%
66%
\newline
(C)
71
%
71 \%
71%
\newline
(D)
81
%
81 \%
81%
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The winter clothing drive has received donations of
5
5
5
coats,
23
23
23
pairs of gloves,
19
19
19
scarves, and
3
3
3
hats so far.
\newline
Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
23
23
23
\newline
(B)
0
0
0
.
27
27
27
\newline
(C)
0
0
0
.
46
46
46
\newline
(D)
0
0
0
.
54
54
54
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Stephen read
12
12
12
books,
20
20
20
magazines, and
17
17
17
newspaper articles last year.
\newline
Based on this data, what is a reasonable estimate of the probability that Stephen's next reading material is a magazine? Choose the best answer.
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
20
20
20
\newline
(B)
0
0
0
.
24
24
24
\newline
(C)
0
0
0
.
35
35
35
\newline
(D)
0
0
0
.
41
41
41
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A restaurant has an electronic system that randomly selects customers when they pay for their meal to receive a coupon for their next visit. Each customer has a
10
%
10 \%
10%
probability of being selected to receive a coupon, and one customer being selected or not doesn't affect whether or not another customer will be selected.
\newline
Suppose that
2
2
2
customers pay for their meals, one after the other.
\newline
What is the probability that NEITHER customer is selected to receive a coupon?
\newline
Round your answer to two decimal places.
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An airport has an electronic system that randomly selects bags for extra security screening. Each bag has a
14
%
14 \%
14%
probability of being selected for extra screening, and one bag being selected or not doesn't affect whether or not another bag will be selected.
\newline
Suppose that
2
2
2
bags go through the system, one after the other.
\newline
What is the probability that both bags are selected for extra screening?
\newline
Round your answer to two decimal places.
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A standard deck of cards has
52
52
52
total cards divided evenly into
4
4
4
suits - there are
13
13
13
clubs,
13
13
13
diamonds,
13
13
13
hearts, and
13
13
13
spades.
\newline
Ayana and Emil are playing a game that involves drawing
2
2
2
cards from a standard deck without replacement to start the game. If neither of the cards are spades, then Ayana goes first. Otherwise, Emil goes first.
\newline
Is this a fair way to decide who goes first? Why or why not?
\newline
Choose
1
1
1
answer:
\newline
(A) No, there is a higher probability that Ayana goes first.
\newline
(B) No, there is a higher probability that Emil goes first.
\newline
(C) Yes, they both have an equal probability of going first.
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