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Math Problems
Algebra 2
Find probabilities using the addition rule
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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In a large
1
Q
1Q
1
Q
question bank,
50
%
50\%
50%
of the questions carry
1
1
1
mark,
30
%
30\%
30%
carry
2
2
2
marks and the rest carry
5
5
5
marks. Questions are chosen from the question bank to test Wendy's IQ. The probabilities for Wendy to correctly answer a question carrying
1
1
1
mark,
2
2
2
marks and
5
5
5
marks are
0.9
0.9
0.9
,
50
%
50\%
50%
0
0
0
and
50
%
50\%
50%
1
1
1
respectively. (a) If a question is chosen randomly, find the probability that Wendy answers it correctly. (b)
50
%
50\%
50%
2
2
2
questions are chosen randomly. (i) Find the probability that Wendy answers at most
5
5
5
questions correctly. (ii) Find the probability that
5
5
5
questions of
1
1
1
mark,
50
%
50\%
50%
6
6
6
questions of
2
2
2
marks and
2
2
2
questions of
5
5
5
marks are chosen. (iii) It is given that
5
5
5
questions of
1
1
1
mark,
50
%
50\%
50%
6
6
6
questions of
2
2
2
marks and
2
2
2
questions of
5
5
5
marks are chosen. Find the probability that Wendy answers exactly
5
5
5
questions correctly and exactly
1
1
1
7
7
7
of them carry
1
1
1
mark.
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Ex
9
9
9
\newline
There are
6
6
6
balls numbered
1
1
1
to
6
6
6
individually in a box.
\newline
Lambda player of a game draws
3
3
3
balls from the box at random. The largest number on the balls drawn is denoted by
\newline
X
X
X
.
\newline
(a) Represent the probability distribution of
\newline
X
X
X
by a table.
\newline
(b) Find
\newline
E
(
X
)
E(X)
E
(
X
)
and
\newline
Var
(
X
)
\text{Var}(X)
Var
(
X
)
.
\newline
(c) Given that
\newline
X
=
4
X=4
X
=
4
, find the probability that the smallest number on the balls drawn is
1
1
1
.
\newline
(d) A player pays
\newline
1
1
1
0
0
0
for each game and gets
\newline
1
1
1
1
1
1
. Find the expected gain or loss if he/she plays
1
1
1
2
2
2
games.
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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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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 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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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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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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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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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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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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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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\newline
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s.moo
303
303
303
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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.
\newline
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.
\newline
What is
P
(
W
)
P(W)
P
(
W
)
, the probability that a junior wears a watch?
7
/
12
7 / 12
7/12
\newline
What is
P
(
E
)
P(E)
P
(
E
)
, the probability that a junior wears earrings?
13
/
24
13 / 24
13/24
\newline
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
\newline
What is
P
(
W
P(W
P
(
W
or
E
)
E)
E
)
, the probability that a junior wears a watch or earrings?
\newline
Show Calculator
\newline
4
4
4
of
4
4
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.
\newline
(f) (i) At any given instant, find the probability that point
C
\mathrm{C}
C
is visible from Tim's window.
\newline
The wind speed increases. The blades rotate at twice the speed, but still at a constant rate.
\newline
(ii) At any given instant, find the probability that Tim can see point
C
\mathrm{C}
C
from his window. Justify your answer.
\newline
[
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?
\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
\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
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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
?
\newline
A.
2
2
2
\newline
B.
5
5
5
\newline
C.
10
10
10
\newline
D.
30
30
30
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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
?
\newline
A.
2
2
2
\newline
B.
5
5
5
\newline
C.
10
10
10
\newline
D.
30
30
30
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This table gives information about a group of students.
\newline
\begin{tabular}{|c|c|c|}
\newline
\hline & Wear glasses & \begin{tabular}{l}
\newline
Do not wear \\
\newline
glasses
\newline
\end{tabular} \\
\newline
\hline Male &
6
6
6
&
11
11
11
\\
\newline
\hline Female &
9
9
9
&
16
16
16
\\
\newline
\hline
\newline
\end{tabular}
\newline
(a) A student is selected at random from the group.
\newline
Find, as a fraction in its lowest terms, the probability that the student is
\newline
(i) a male who wears glasses, I/
\newline
(ii) a female who does not wear glasses. /
1
1
1
\newline
(b) Two students are selected at random from the group.
\newline
Find the probability that
\newline
(i) one is a male and one is a female,
\newline
(ii) at least one is a male who wears glasses.
=
15
=15
=
15
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6
6
6
. A box contains
6
6
6
red cards,
5
5
5
blue cards and
9
9
9
yellow cards.
\newline
The cards are identical except for the colours.
\newline
Two cards are taken from the box without replacement.
\newline
(a) Draw a tree diagram to show the probabilities of the possible outcomes.
\newline
(b) Find, as a fraction in its simplest form, the probability that
\newline
(i) the two cards are of the same colour,
\newline
(ii) at least one of the cards is yellow.
\newline
(c) A third card is taken from the box.
\newline
Find, as a fraction in its simplest form, the probability that exactly two of the cards is blue.
\newline
Firstcad
\newline
Secend card
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A movie studio surveyed married couples about the types of movies they prefer.
\newline
In the survey, the husband and wife were each asked if they prefer action, comedy, or drama.
\newline
Here is a summary of the data the studio got after asking
75
75
75
couples.
\newline
\begin{tabular}{|c|c|c|}
\newline
\hline Husband & Wife & \begin{tabular}{c}
\newline
Number of \\
\newline
couples
\newline
\end{tabular} \\
\newline
\hline action & action &
7
7
7
\\
\newline
\hline action & comedy &
13
13
13
\\
\newline
\hline action & drama &
5
5
5
\\
\newline
\hline comedy & action &
9
9
9
\\
\newline
\hline comedy & comedy &
4
4
4
\\
\newline
\hline comedy & drama &
9
9
9
\\
\newline
\hline drama & action &
10
10
10
\\
\newline
\hline drama & comedy &
12
12
12
\\
\newline
\hline drama & drama &
6
6
6
\\
\newline
\hline
\newline
\end{tabular}
\newline
Suppose the movie studio will ask
100
100
100
more couples about their movie preferences.
\newline
How many of these
100
100
100
couples will have at most one spouse prefer drama movies? Use the data to make a prediction.
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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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9
9
9
. Six discs, numbered from
1
1
1
to
6
6
6
, are placed in a bag. Two discs are drawn at random from the bag and placed side by side to form a two-digit number where the first number drawn is the digit in the tens place.
\newline
(i) Display all the outcomes of the experiment using a possibility diagram.
\newline
(ii) Using the possibility diagram, find the probability that the number formed is
\newline
(a) divisible by
2
2
2
,
\newline
(b) divisible by
5
5
5
,
\newline
(c) a prime number,
\newline
(d) a perfect square.
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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
Get tutor help
Chapter
16
16
16
\newline
- (
20
20
20
points) Question
1
1
1
: In order to test a theory that coffee consumption can have an effect on test scores, a researcher conducts a study on a group of adults. Each is given a test. Then for one week, each subject is required to consume a certain amount of coffee; then he or she is retested. The results are shown here.
\newline
\begin{tabular}{c|c}
\newline
\hline Score Before & Score After \\
\newline
\hline
109
109
109
&
106
106
106
\\
\newline
116
116
116
&
123
123
123
\\
\newline
123
123
123
&
122
122
122
\\
\newline
114
114
114
&
119
119
119
\\
\newline
107
107
107
&
106
106
106
\\
\newline
105
105
105
&
107
107
107
\\
\newline
115
115
115
&
114
114
114
\\
\newline
95
95
95
&
98
98
98
\\
\newline
111
111
111
&
95
95
95
\\
\newline
98
98
98
&
97
97
97
\\
\newline
\hline
\newline
\end{tabular}
\newline
1
1
1
. Test the claim that coffee improves test score. Use WRS and
α
\alpha
α
=
0.01
=0.01
=
0.01
.
\newline
- Solution :
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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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35
35
35
. In an examination, the mean score of the students who passed is
71
71
71
and the mean score of the students who failed is
42
42
42
. If the overall mean score of the students is
59
59
59
.
4
4
4
, find the percentage of students who passed in the examination.
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Question
\newline
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. 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
, what is the rejection region?
\newline
Use the graph below to show the rejection region. First, move the blue dot to choose the appropriate test (left-, right, or twotailed). Then, slide the shaded region(s) to represent the rejection region.
\newline
Provide your answer below:
\newline
Move the blue dot to choose the appropriate test
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Question
\newline
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
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
There is a
5
%
5 \%
5%
chance of rejecting the null hypothesis.
\newline
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
There is a
5
%
5 \%
5%
chance that
μ
>
60
\mu>60
μ
>
60
.
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A newborn calf weighs
40
kilograms
40\,\text{kilograms}
40
kilograms
. Each week its weight increases by
5
%
5\%
5%
. Let
W
W
W
be the weight in kilograms of the calf after
n
n
n
weeks. Which of the following best explains the relationship between
W
W
W
and
n
n
n
?
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11
11
11
.
6
6
6
HW - Events
\newline
Question
10
10
10
,
11
11
11
.
6
6
6
.
5
5
5
\newline
HW Score:
91.67
%
,
27.5
91.67 \%, 27.5
91.67%
,
27.5
of
30
30
30
\newline
points
\newline
Points:
1
1
1
of
1
1
1
\newline
Save
\newline
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
6
13
\frac{6}{13}
13
6
\newline
(Type an integer or a simplified fraction.)
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1
2
3
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