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Algebra 2
Find probabilities using the addition rule
In a certain Algebra
2
2
2
class of
24
24
24
students,
16
16
16
of them play basketball and
7
7
7
of them play baseball. There are
5
5
5
students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
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In a certain Algebra
2
2
2
class of
23
23
23
students,
15
15
15
of them play basketball and
16
16
16
of them play baseball. There are
3
3
3
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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At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender.
\newline
The probability that a competitor reacted in over
0.7
0.7
0.7
seconds is
0.6
0.6
0.6
, the probability that a competitor was female is
0.4
0.4
0.4
, and the probability that a competitor reacted in over
0.7
0.7
0.7
seconds and was female is
0.3
0.3
0.3
.
\newline
What is the probability that a randomly chosen competitor reacted in over
0.7
0.7
0.7
seconds or was female?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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This season, the probability that the Yankees will win a game is
0.61
0.61
0.61
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0.49
0.49
0.49
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0.3
0.3
0.3
. 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.
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Put the following equation of a line into slope-intercept form, simplifying all fractions.
\newline
12
x
−
20
y
=
−
100
12x-20y=-100
12
x
−
20
y
=
−
100
\newline
Answer
\newline
◻
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A light-year is the distance that light can travel in one year. The Andromeda Galaxy,
2.5
×
1
0
6
2.5 \times 10^6
2.5
×
1
0
6
light-years away from Earth, is the brightest galaxy that can be seen with the naked eye. The closest galaxy to Earth is the Canis Major Dwarf Galaxy. Though it is only about
2.5
×
1
0
4
2.5 \times 10^4
2.5
×
1
0
4
light-years away, it can only be seen with a telescope. Use these numbers to complete the sentence below. Write your answer in standard form, without using exponents. The Canis Major Dwarf Galaxy is about ____ times as far away as the Andromeda Galaxy.
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Each time she throws a dart, the probability that Mary hits the dartboard is
\newline
2
7
\frac{2}{7}
7
2
.
\newline
She throws two darts, one after the other.
\newline
What is the probability that she hits the dartboard with both darts?
\newline
(A)
1
21
\frac{1}{21}
21
1
\newline
(B)
4
49
\frac{4}{49}
49
4
\newline
(C)
2
7
\frac{2}{7}
7
2
\newline
(D)
4
7
\frac{4}{7}
7
4
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A birthday party caterer counted the number of juice cups on the table. The cups contained different flavored juices and different shaped straws.
\newline
The probability that a cup contains pineapple juice is
0.7
0.7
0.7
, the probability that it contains a regular straw is
0.6
0.6
0.6
, and the probability that it contains pineapple juice and contains a regular straw is
0.4
0.4
0.4
.
\newline
What is the probability that a randomly chosen cup contains pineapple juice or contains a regular straw?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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Samir works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Samir to surprise them with the flavor. The teas are categorized by flavor and caffeine level.
\newline
The probability that a tea is fruity is
0.2
0.2
0.2
, the probability that it is caffeine-free is
0.4
0.4
0.4
, and the probability that it is fruity and caffeine-free is
0.1
0.1
0.1
.
\newline
What is the probability that a randomly chosen tea is fruity or caffeine-free?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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Frank and his brother are at a store shopping for a beanbag chair for their school's library. The store sells beanbag chairs with different fabrics and types of filling.
\newline
The probability that a beanbag chair is made from suede is
0.6
0.6
0.6
, the probability that it is filled with beads is
0.2
0.2
0.2
, and the probability that it is made from suede and is filled with beads is
0.1
0.1
0.1
.
\newline
What is the probability that a randomly chosen beanbag chair is made from suede or is filled with beads?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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Emilio just returned from a spring break volunteer trip. He is shopping for a photo album that will showcase his photos from the trip. The albums range in photo capacity and orientation.
\newline
The probability that a photo album holds under
200
200
200
photos is
0.7
0.7
0.7
, the probability that it is oriented horizontally is
0.3
0.3
0.3
, and the probability that it holds under
200
200
200
photos and is oriented horizontally is
0.2
0.2
0.2
.
\newline
What is the probability that a randomly chosen photo album holds under
200
200
200
photos or is oriented horizontally?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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A skating rink attendant monitored the number of injuries at the rink over the past year. He tracked the ages of those injured and the kinds of skates worn during injury.
\newline
The probability that an injured skater was a minor is
0.8
0.8
0.8
, the probability that an injured skater was wearing in-line skates is
0.3
0.3
0.3
, and the probability that an injured skater was a minor and was wearing in-line skates is
0.2
0.2
0.2
.
\newline
What is the probability that a randomly chosen injured skater was a minor or was wearing in-line skates?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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On a camping trip, Whitney kept a log of the types of snakes she saw. She noted their colors and approximate lengths.
\newline
The probability that a snake is brown is
0.4
0.4
0.4
, the probability that it is under
1
1
1
foot long is
0.9
0.9
0.9
, and the probability that it is brown and under
1
1
1
foot long is
0.3
0.3
0.3
.
\newline
What is the probability that a randomly chosen snake is brown or under
1
1
1
foot long?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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A large random sample of adults ages
25
25
25
to
40
40
40
living in Kansas City, Missouri was asked whether they plan to purchase a new cell phone sometime in the next year. The results of the survey are most representative of which of the following populations?
\newline
Choose
1
1
1
answer:
\newline
(A) Adults ages
25
25
25
to
40
40
40
living in Kansas City, Missouri
\newline
(B) Adults living in Kansas City, Missouri
\newline
(C) Adults ages
25
25
25
to
40
40
40
living in Missouri
\newline
(D) Adults living in the US
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F
=
(
K
−
273.15
)
⋅
1.8
+
32.00
F=(K-273.15) \cdot 1.8+32.00
F
=
(
K
−
273.15
)
⋅
1.8
+
32.00
\newline
An equation for temperature conversion from
K
K
K
degrees Kelvin to
F
F
F
degrees Fahrenheit is given by the equation. What is the significance of
273
273
273
.
15
15
15
in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A) A temperature of
273
273
273
.
15
15
15
Kelvin degrees converts to
0
0
0
Fahrenheit degrees.
\newline
(B) A temperature of
−
273
-273
−
273
.
15
15
15
Kelvin degrees converts to
0
0
0
Fahrenheit degrees.
\newline
(C) A temperature of
273
273
273
.
15
15
15
Kelvin degrees converts to
32
32
32
Fahrenheit degrees.
\newline
(D) A temperature of
−
273
-273
−
273
.
15
15
15
Kelvin degrees converts to
32
32
32
Fahrenheit degrees.
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You've decided you want a plant for your room. At the gardening store, there are
4
4
4
different kinds of plants (tulip, fern, cactus, and ficus) and
4
4
4
different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
\newline
If you randomly pick the plant and the pot, what is the probability that you won't get a clay pot or a cactus?
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You're playing a game where you defend your village from an orc invasion. There are
3
3
3
characters (elf, hobbit, or human) and
5
5
5
defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.
\newline
If you randomly choose your character and tool, what is the probability that you won't be a hobbit or use an umbrella?
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Justin lives in Saint Paul and goes to school in Minneapolis. In the morning, he has
3
3
3
transportation options (bus, cab, or train) to school, and in the evening he has the same
3
3
3
choices for his trip home.
\newline
If Justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?
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Marvin lives in Stormwind City and works as an engineer in the city of Ironforge. In the morning, he has
3
3
3
transportation options (teleport, ride a dragon, or walk) to work, and in the evening he has the same
3
3
3
choices for his trip home.
\newline
If Marvin randomly chooses his method of travel in the morning and in the evening, what is the probability that he teleports at least once per day?
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Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has
3
3
3
transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same
3
3
3
choices for her trip home.
\newline
If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?
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James lives in San Francisco and works in Mountain View. In the morning, he has
3
3
3
transportation options (bus, cab, or train) to work, and in the evening he has the same
3
3
3
choices for his trip home.
\newline
If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?
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A technology company is studying the launch of their new laptop computers in order to track warranty purchases. The company states the average warranty length for their products is longer than
60
60
60
days.
\newline
If we would like to test the company's claim with a hypothesis test using a significance level of
α
=
0.05
\alpha=0.05
α
=
0.05
, which of the following choices are true?
\newline
Select the correct answer below:
\newline
A)There is a
5
%
5 \%
5%
chance we will conclude
μ
=
60
\mu=60
μ
=
60
, but is in fact
μ
>
60
\mu>60
μ
>
60
.
\newline
B)There is a
5
%
5 \%
5%
chance of rejecting the null hypothesis.
\newline
C)There is a
5
%
5 \%
5%
chance we will conclude
μ
>
60
\mu>60
μ
>
60
, but is in fact
μ
=
60
\mu=60
μ
=
60
.
\newline
D)There is a
5
%
5 \%
5%
chance that
μ
>
60
\mu>60
μ
>
60
.
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Spinner
R
R
R
determines the digit in the tens place, and Spinner
T
T
T
determines the digit in the ones place. What is the probability that the two-digit number determined by spinning each spinner one time is an even number?
\newline
A.
1
2
\frac{1}{2}
2
1
\newline
B.
1
4
\frac{1}{4}
4
1
\newline
C.
5
16
\frac{5}{16}
16
5
\newline
D.
1
8
\frac{1}{8}
8
1
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Alang has a bag that contains pineapple chews, strawberry chews, and lime chews. He performs an experiment. Alang randomly removes a chew from the bag, records the result, and returns the chew to the bag. Alang performs the experiment
26
26
26
times. The results are shown below:
\newline
A pineapple chew was selected
20
20
20
times.
\newline
A strawberry chew was selected
4
4
4
times.
\newline
A lime chew was selected
2
2
2
times.
\newline
Based on these results, express the probability that the next chew Alang removes from the bag will be lime chew as a fraction in simplest form.
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You are dealt one card from a
52
52
52
- card deck. Find the probability that you are not dealt a card with number from
2
2
2
to
8
8
8
.
\newline
The probability is
_
_
_
_
_
\_\_\_\_\_
_____
.
\newline
(Type an integer or a simplified fraction.)
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You are a space alien. You visit planet Earth and abduct
97
97
97
chickens,
47
47
47
cows, and
77
77
77
humans. Then, you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected.
\newline
Create a probability model to show how likely you are to select each type of Earth creature.
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Katherine is playing a board game. The probability that Katherine will lose a turn on her next turn is
4
5
\frac{4}{5}
5
4
. Which word or phrase describes the probability that Katherine will lose a turn?
\newline
certain
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
likely
\newline
impossible
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Alexa buys a ticket for a raffle with several prizes. The probability that she wins a prize is
88
%
88 \%
88%
. Which word or phrase describes the probability that Alexa will win a prize?
\newline
likely
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
certain
\newline
unlikely
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Jin is playing a board game. The probability that Jin will lose a turn on his next turn is
50
%
50 \%
50%
. Which word or phrase describes the probability that Jin will lose a turn?
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
unlikely
\newline
likely
\newline
certain
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Ariana is playing a board game. The probability that Ariana will lose a turn on her next turn is
1
5
\frac{1}{5}
5
1
. Which word or phrase describes the probability that Ariana will lose a turn?
\newline
likely
\newline
impossible
\newline
unlikely
\newline
an equal chance or
50
50
50
−
50
-50
−
50
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Liam is playing a board game. The probability that Liam will lose a turn on his next turn is
12
%
12 \%
12%
. Which word or phrase describes the probability that Liam will lose a turn?
\newline
an equal chance or
50
50
50
−
50
-50
−
50
\newline
unlikely
\newline
likely
\newline
impossible
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Hailey rolls a standard six-sided die, numbered from
1
1
1
to
6
6
6
. Which word or phrase describes the probability that she will roll a
7
7
7
?
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
certain
\newline
impossible
\newline
unlikely
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Samantha has a bag of candy full of
10
10
10
strawberry chews and
10
10
10
cherry chews that she eats one at a time. Which word or phrase describes the probability that she reaches in without looking and pulls out a cherry chew?
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
impossible
\newline
certain
\newline
likely
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Kaylee has a bag of candy full of
3
3
3
strawberry chews and
17
17
17
cherry chews that she eats one at a time. Which word or phrase describes the probability that she reaches in without looking and pulls out a cherry chew?
\newline
impossible
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
likely
\newline
certain
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Lincoln has a bag of candy full of
10
10
10
strawberry chews and
10
10
10
cherry chews that he eats one at a time. Which word or phrase describes the probability that he reaches in without looking and pulls out a banana chew?
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
certain
\newline
likely
\newline
impossible
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Madelyn has a bag of candy full of
19
19
19
strawberry chews and
1
1
1
cherry chew that she eats one at a time. Which word or phrase describes the probability that she reaches in without looking and pulls out a strawberry chew?
\newline
unlikely
\newline
likely
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
certain
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The weather forecaster says that tomorrow there is a
0
%
0 \%
0%
chance that it will rain. Which word or phrase describes the probability that it will rain?
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
likely
\newline
impossible
\newline
unlikely
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Brianna buys a ticket for a raffle with several prizes. The probability that she wins a prize is
1
8
\frac{1}{8}
8
1
. Which word or phrase describes the probability that Brianna will win a prize?
\newline
likely
\newline
impossible
\newline
unlikely
\newline
an equal chance or
50
50
50
−
50
-50
−
50
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Sophie buys a ticket for a raffle with several prizes. The probability that she wins a prize is
4
5
\frac{4}{5}
5
4
. Which word or phrase describes the probability that Sophie will win a prize?
\newline
likely
\newline
certain
\newline
an equal chance or
50
50
50
−
50
-50
−
50
\newline
impossible
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The weather forecaster says that tomorrow there is a
2
%
2 \%
2%
chance that it will rain. Which word or phrase describes the probability that it will rain?
\newline
impossible
\newline
likely
\newline
unlikely
\newline
an equal chance or
50
50
50
−
50
-50
−
50
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Elizabeth has a bag of candy full of
17
17
17
strawberry chews and
3
3
3
cherry chews that she eats one at a time. Which word or phrase describes the probability that she reaches in without looking and pulls out a strawberry chew?
\newline
likely
\newline
impossible
\newline
an equal chance or
50
−
50
50-50
50
−
50
\newline
certain
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The yield on
1
1
1
-year Treasury securities is
6
%
6\%
6%
,
2
2
2
-year securities yield
6.2
%
6.2\%
6.2%
,
3
3
3
-year securities yield
6.3
%
6.3\%
6.3%
, and
4
4
4
-year securities yield
6.5
%
6.5\%
6.5%
. There is no maturity risk premium. Using expectations theory and geometric averages, forecast the yields on the following securities: A
2
2
2
-year security,
1
1
1
year from now?
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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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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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