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Math Problems
Algebra 2
Find probabilities using the addition rule
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Gabriella sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
27
27
27
visitors purchased no costume.
75
75
75
visitors purchased exactly one costume.
11
11
11
visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase more than one costume as a fraction in simplest form.
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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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In a certain Algebra
2
2
2
class of
24
24
24
students,
16
16
16
of them play basketball and
10
10
10
of them play baseball. There are
7
7
7
students who play both sports. 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
27
27
27
students,
6
6
6
of them play basketball and
18
18
18
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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2
2
2
. You are thinking of using a
t
t
t
procedure to test hypotheses about the mean of a population using a significance level of
0
0
0
.
05
05
05
. You suspect that the distribution of the population is not Normal and may be moderately skewed. Which of the following statements is correct?
\newline
(a) You should not use the
t
t
t
procedure because the population does not have a Normal distribution.
\newline
(b) You may use the
t
t
t
procedure as long as your sample size is at least
30
30
30
.
\newline
(c) You may use the
t
t
t
procedure, but you should probably claim only that the significance level is
0
0
0
.
10
10
10
.
\newline
(d) You may not use the
t
t
t
procedure unless the sample size is less than
30
30
30
.
\newline
(e) You may use the
t
t
t
procedure as long as there are no outliers.
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In a class of
24
24
24
students,
14
14
14
have a cat and
5
5
5
have a dog. There are
2
2
2
students who have a cat and a dog. What is the probability that a student has a cat given that they do not have a dog?
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In a math class with
20
20
20
students, a test was given the same day that an assignment was due. There were
13
13
13
students who passed the test and
12
12
12
students who completed the assignment. There were
10
10
10
students who passed the test and also completed the assignment. What is the probability that a student completed the assignment given that they passed the test?
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This season, the probability that the Yankees will win a game is
0
0
0
.
59
59
59
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 lose and score fewer than
5
5
5
runs is o.
33
33
33
. 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.
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This season, the probability that the Yankees will win a game is
0
0
0
.
46
46
46
and the probability that the Yankees will score
5
5
5
or more runs in a game is o.
57
57
57
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
35
35
35
. What is the probability that the Yankees would score
5
5
5
or more runs when they win the game? Round your answer to the nearest thousandth.
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This season, the probability that the Yankees will win a game is
0
0
0
.
49
49
49
and the probability that the Yankees will score
5
5
5
or more runs in a game is o.
54
54
54
. The probability that the Yankees lose and score fewer than
5
5
5
runs is o.
36
36
36
. What is the probability that the Yankees will win when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
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Nia is
1
1
1
of
n
n
n
students in a class. Every month, Nia's teacher randomly selects
4
4
4
students from their class to act as class president, vice president, secretary, and treasurer. No one student can hold two positions. In a given month, what is the probability that Nia is chosen as president?
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IV. Use the chart in the discussion to answer these questions:
\newline
a. What is the probability a day in the
70
70
70
s is a Monday?
\newline
b. Which set forms the intersection of Tuesdays in the
80
80
80
s?
\newline
c. What is the probability an observation picked at random is both a Sunday and
\newline
V. Construct a histogram to display the temperature frequencies for the month. (Use ter totals.)
\newline
VI. Pretend that you are working for the tourist bureau for your city. Which measure of
c
\mathrm{c}
c
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Four children are bor in a family. Assume that the likelihood of a child being bom male is the same is it is for being born female. What is the probability that the four children, born will be all girls? Draw a tree diagram or list a sample space that justifies your answer.
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In Mr. Von Yazdee's Algebra II class, the probability a student completed the homework is
0.5
0.5
0.5
, and the probability they passed the test is
0.6
0.6
0.6
. If the probability that a student passed the test given, they completed is the homework is
0.8
0.8
0.8
, find the probability that a student passed the test and completed the homework to the nearest percent.
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Each card in a standard deck of playing cards is unique and belongs to one of four suits: thirteen cards are clubs thirteen cards are diamonds thirteen cards are hearts thirteen cards are spades Suppose that Luisa randomly draws five cards without replacement. What is the probability that Luisa gets three diamonds and two hearts (in any order)? Choose
1
1
1
answer:
\newline
Choose
1
1
1
answer:
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Lin and Kai are friends that work together on a team of
n
n
n
total people. Their manager is going to randomly select
m
m
m
people from the team of
n
n
n
to attend a conference. What is the probability that Lin and Kai are the
m
m
m
people chosen?
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randomly select seven U.S. adults. Find the probability that the number who have very little confidence in newspapers is (a) exactly six and (b) exactly four.
\newline
(a) The probability that the number who have very little confidence in newspapers is exactly six is
0.0183
0.0183
0.0183
.
\newline
(Round to three decimal places as needed.)
\newline
0.0183
0.0183
0.0183
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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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part
2
2
2
: Carnival Games
\newline
1
1
1
) (
7
7
7
points) If you have been to a carnival or fair, you may remember a game where you throw a dart at a wall of balloons to pop them. Here is a similar game:
\newline
- There are
30
30
30
balloons on the wall.
\newline
-
10
10
10
of them contain prize tokens.
\newline
- The player pays
$
2
\$ 2
$2
and gets to throw darts until
2
2
2
balloons pop. don't win anything.
\newline
Let's find the expected value for this game.
\newline
In order to fill in the table below, first complete the tree diagram, using fractions to label the probabilities on each branch and the final probabilities (w).
\newline
Now use the probabilities you found to fill in the table and compute the expected value of this game.
\newline
\begin{tabular}{|c|c|c|c|c|}
\newline
\hline \begin{tabular}{c}
\newline
Number of \\
\newline
tokens
\newline
\end{tabular} & \begin{tabular}{c}
\newline
Probability \\
\newline
(use fractions)
\newline
\end{tabular} & Payout & \begin{tabular}{c}
\newline
Value \\
\newline
(payout - \$\(2\) cost)\(\newline\)\end{tabular} & \begin{tabular}{c} \(\newline\)Weighted Value for the \\\(\newline\)player: \\\(\newline\)(use decimals, rounded to the \\\(\newline\)nearest penny)\(\newline\)\end{tabular} \\\(\newline\)\hline \(0\) & & \( \$ 0 \) & & \\\(\newline\)\hline \(1\) & & \( \$ 3 \) & & \\\(\newline\)\hline \(2\) & & \( \$ 4 \) & & \\\(\newline\)\hline \multicolumn{\(5\)}{|c|}{ Total Expected Value (Payout) for the player: } \\\(\newline\)\hline\(\newline\)\end{tabular}\(\newline\)Does the game favor the player or the game-runner? Explain.
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c. What is meant by correlation between two variables
x
x
x
and
y
y
y
.
\newline
ii. Write the mathematical formula for correlation between two variables.
\newline
d. A sample of ten (
10
10
10
) families in an area revealed the following figures for family size and the amount spent on food in a certain weck.
\newline
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\newline
\hline \begin{tabular}{l}
\newline
Family \\
\newline
size (x)
\newline
\end{tabular} &
3
3
3
&
6
6
6
&
5
5
5
&
6
6
6
&
6
6
6
&
3
3
3
&
4
4
4
&
4
4
4
&
5
5
5
&
3
3
3
\\
\newline
\hline \begin{tabular}{l}
\newline
Amount \\
\newline
spent on \\
\newline
food
(
y
)
(\mathrm{y})
(
y
)
\newline
\end{tabular} &
9
9
9
&
10
10
10
&
15
15
15
&
13
13
13
&
14
14
14
&
11
11
11
&
7
7
7
&
9
9
9
&
19
19
19
&
9
9
9
\\
\newline
\hline
\newline
\end{tabular}
\newline
i. Compute the coefficient of correlation between
x
\mathrm{x}
x
and
y
\mathrm{y}
y
.
\newline
ii. Derive the line of regression between
x
x
x
and
y
y
y
.
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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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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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15
15
15
. You are buying plants and soil for your garden. The soil costs
$
4.00
\$ 4.00
$4.00
per bag and the plants cost
$
10.00
\$ 10.00
$10.00
each. You want to buy at least
5
5
5
plants and can spend no more than
$
100
\$ 100
$100
total.
\newline
a. Write a system of linear inequalities to model the situation.
\newline
b. Graph the system of linear inequalities.
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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 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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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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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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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 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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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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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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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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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 girl flips a coin and rolls a
6
6
6
-sided die
50
50
50
times. The outcome that she gets a tail and rolls a
1
1
1
occurs
7
7
7
times. Calculate the experimental probability and the theoretical probability of having the outcome of tail and
1
1
1
.
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A baseball player has a batting average of
0.205
0.205
0.205
. What is the probability that he has exactly
1
1
1
hits in his next
7
7
7
at bats? The probability is
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18
18
18
is divisible by both
2
2
2
and
3
3
3
. It is also divisible by
2
×
3
=
6
2 \times 3=6
2
×
3
=
6
. Similarly, a number is divisible by both
4
4
4
and
6
6
6
. Can we say that the number must also be divisible by
4
×
6
=
24
4 \times 6=24
4
×
6
=
24
? If not, give an example to justify your answer.
\newline
I am the smallest number, having four different prime factors. Can you find me?
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A college bookstore makes an order to replenish its stock of three different types of paper: college rule line paper, legal rule line paper, and graph paper. In addition, the paper is purchased bound as either spiral notebooks or paper pads. The table shows the store's order.
\newline
Bookstore Order of Different Types of Paper
\newline
\begin{tabular}{lccc}
\newline
& College rule & Legal rule & Graph \\
\newline
\hline Spiral notebooks &
175
175
175
&
60
60
60
&
75
75
75
\\
\newline
Paper pads &
90
90
90
&
110
110
110
&
125
125
125
\newline
\end{tabular}
\newline
If a graph paper item from the order is selected at random, what is the percent probability that the item is bound as a paper pad?
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A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers. The consulting company gathered data from each customer who purchased hiking shoes, and recorded the shoe brand and the customer's level of happiness.
\newline
\begin{tabular}{|l|c|c|}
\newline
\hline & A Footlong shoe & A Toes Knows shoe \\
\newline
\hline Displeased &
3
3
3
&
3
3
3
\\
\newline
\hline Pleased &
3
3
3
&
3
3
3
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected customer is pleased or purchased a Toes Knows shoe?
\newline
Simplify any fractions.
\newline
□
\square
□
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\newline
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There are
600
600
600
students in a high school junior class. Of these
600
600
600
students,
350
350
350
regularly wear a watch to school,
325
325
325
regularly wear earrings, and
300
300
300
regularly wear a watch and earrings. Using this information, answer each of the following questions.
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Let
W
W
W
be the event that a randomly selected junior regularly wears a watch and
E
E
E
be the event that a randomly selected junior regularly wears earrings.
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What is
P
(
W
)
P(W)
P
(
W
)
, the probability that a junior wears a watch?
7
/
12
7 / 12
7/12
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What is
P
(
E
)
P(E)
P
(
E
)
, the probability that a junior wears earrings?
13
/
24
13 / 24
13/24
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What is
P
(
W
P(W
P
(
W
and
E
)
E)
E
)
, the probability that a junior wears a watch and earrings?
1
/
2
1 / 2
1/2
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What is
P
(
W
P(W
P
(
W
or
E
)
E)
E
)
, the probability that a junior wears a watch or earrings?
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4
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Looking through his window, Tim has a partial view of the rotating wind turbine. The position of his window means that he cannot see any part of the wind turbine that is more than
100
m
100 \mathrm{~m}
100
m
above the ground. This is illustrated in the following diagram.
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(f) (i) At any given instant, find the probability that point
C
\mathrm{C}
C
is visible from Tim's window.
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The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.
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(ii) At any given instant, find the probability that Tim can see point
C
\mathrm{C}
C
from his window. Justify your answer.
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[
5
5
5
]
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You currently drive
240
240
240
miles per week in a car that gets
24
24
24
miles per gallon of gas. You are considering buying a new fuel-efficient car for
$
13
,
000
\$ 13,000
$13
,
000
(after trade-in on your current car) that gets
40
40
40
miles per gallon. Insurance premiums for the new and old car are
$
720
\$ 720
$720
and
$
500
\$ 500
$500
per year, respectively. You anticipate spending
$
1050
\$ 1050
$1050
per year on repairs for the old car and having no repairs on the new car. Assume gas costs
$
2.45
\$ 2.45
$2.45
per gallon. Over a seven-year period, is it less expensive to keep your old car or buy the new car? By how much?
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the new car is
$
3420.08
\$ 3420.08
$3420.08
less expensive
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the old car is
$
3622.80
\$ 3622.80
$3622.80
less expensive
\newline
the new car is
$
3420.08
\$ 3420.08
$3420.08
less expensive
\newline
the old car is
$
3622.80
\$ 3622.80
$3622.80
less expensive
Get tutor help
The probability of drawing a peppermint candy out of a jar of
25
25
25
candies is
1
5
\frac{1}{5}
5
1
. How many more peppermint candies should be added to the jar in order to increase the probability of drawing a peppermint candy to
1
3
\frac{1}{3}
3
1
?
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A.
2
2
2
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B.
5
5
5
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C.
10
10
10
\newline
D.
30
30
30
Get tutor help
The probability of drawing a peppermint candy out of a jar of
25
25
25
candies is
1
5
\frac{1}{5}
5
1
. How many more peppermint candies should be added to the jar in order to increase the probability of drawing a peppermint candy to
1
3
\frac{1}{3}
3
1
?
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A.
2
2
2
\newline
B.
5
5
5
\newline
C.
10
10
10
\newline
D.
30
30
30
Get tutor help
This table gives information about a group of students.
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\begin{tabular}{|c|c|c|}
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\hline & Wear glasses & \begin{tabular}{l}
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Do not wear \\
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glasses
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\end{tabular} \\
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\hline Male &
6
6
6
&
11
11
11
\\
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\hline Female &
9
9
9
&
16
16
16
\\
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\hline
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\end{tabular}
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(a) A student is selected at random from the group.
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Find, as a fraction in its lowest terms, the probability that the student is
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(i) a male who wears glasses, I/
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(ii) a female who does not wear glasses. /
1
1
1
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(b) Two students are selected at random from the group.
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Find the probability that
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(i) one is a male and one is a female,
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(ii) at least one is a male who wears glasses.
=
15
=15
=
15
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