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Math Problems
Algebra 2
Find probabilities using the addition rule
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
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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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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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2
2
2
) The quiz on binomial probability has
5
5
5
multiple-choice questions. Each question has
4
4
4
responses and only one is correct. What is the probability that a student can pass the quiz by guessing all of the answers (to receive a passing grade students need to answer at least
3
3
3
questions correctly)? Write your answer as a percentage.
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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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The table shows the educational attainment of the population in a certain country, ages
25
25
25
and over, expressed in milions. Find the probability that a randomly selected person, aged
25
25
25
or over, has not completed four years (or more) of college
\newline
Male
\newline
Female
\newline
Total
\newline
\begin{tabular}{|c|c|c|c|c|}
\newline
\hline \multicolumn{
2
2
2
}{|c|}{ Years of High School } & \multicolumn{
2
2
2
}{|c|}{ Years of College } & \multirow{
2
2
2
}{*|}{ Total } \\
\newline
\hline Less than
4
4
4
&
4
4
4
only & Some (less than
4
4
4
) &
4
4
4
or more & \\
\newline
\hline
12
12
12
&
24
24
24
&
24
24
24
&
20
20
20
&
80
80
80
\\
\newline
\hline
11
11
11
&
28
28
28
&
18
18
18
&
17
17
17
&
74
74
74
\\
\newline
\hline
23
23
23
&
52
52
52
&
42
42
42
&
37
37
37
&
154
154
154
\\
\newline
\hline
\newline
\end{tabular}
\newline
The probability is
□
\square
□
. (Type an integer or a simplified fraction )
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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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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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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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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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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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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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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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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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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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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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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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Marshall was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Marshall recorded which type of guitar each contestant played. He also counted the number of contestants wearing different kinds of pants, as there were some interesting stylistic choices.
\newline
The probability that a contestant played an electric guitar is
0
0
0
.
8
8
8
, the probability that a contestant was dressed in sequins is
0
0
0
.
4
4
4
, and the probability that a contestant played an electric guitar or was dressed in sequins is
0
0
0
.
9
9
9
.
\newline
What is the probability that a randomly chosen contestant played an electric guitar and was dressed in sequins?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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The research department of a board game company surveyed some shoppers at a local mall. The team asked shoppers how often they read the news, among other questions. Then the team played a memory card game with the shoppers. They recorded how many cards each shopper remembered.
\newline
The probability that a shopper reads the news
3
−
4
3-4
3
−
4
times a week is
0
0
0
.
3
3
3
, the probability that a shopper remembered
4
−
6
4-6
4
−
6
cards is
0
0
0
.
8
8
8
, and the probability that a shopper reads the news
3
3
3
−
4
-4
−
4
times a week or remembered
4
4
4
−
6
-6
−
6
cards is
1
1
1
.
\newline
What is the probability that a randomly chosen shopper reads the news
3
3
3
−
4
-4
−
4
times a week and remembered
4
4
4
−
6
-6
−
6
cards?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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A customer at a sushi restaurant was examining the types of sushi rolls offered on the menu. Rolls vary by type of fish and level of spiciness. Rolls only contain one type of fish.
\newline
The probability that a sushi roll contains crab is
0
0
0
.
8
8
8
, the probability that it is labeled not spicy is
0
0
0
.
8
8
8
, and the probability that it contains crab or is labeled not spicy is
1
1
1
.
\newline
What is the probability that a randomly chosen sushi roll contains crab and is labeled not spicy?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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A creative writing class compiled a list of their favorite superheroes. They listed each superhero's superpower and personality flaw.
\newline
The probability that a superhero can fly is
0
0
0
.
7
7
7
, the probability that a superhero has a dark side is
0
0
0
.
8
8
8
, and the probability that a superhero can fly or has a dark side is
0
0
0
.
9
9
9
.
\newline
What is the probability that a randomly chosen superhero can fly and has a dark side?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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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
0
0
.
7
7
7
seconds is
0
0
0
.
6
6
6
, the probability that a competitor was female is
0
0
0
.
4
4
4
, and the probability that a competitor reacted in over
0
0
0
.
7
7
7
seconds and was female is
0
0
0
.
3
3
3
.
\newline
What is the probability that a randomly chosen competitor reacted in over
0
0
0
.
7
7
7
seconds or was female?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
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probability it will rain is
0
0
0
.
35
35
35
find the probability it will rain on
3
3
3
consecutive out of
10
10
10
days
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Question
13
13
13
,
11
11
11
.
5
5
5
.
15
15
15
\newline
HW score:
\newline
92.06
%
92.06\%
92.06%
,
19.33
19.33
19.33
of
\newline
part
2
2
2
of
3
3
3
\newline
21
21
21
points
\newline
Points:
0.33
0.33
0.33
of
1
1
1
\newline
Save
\newline
A hand consists of
4
4
4
cards from a well-shuffled deck of
52
52
52
cards.
\newline
a. Find the total number of possible
4
4
4
-card poker hands
\newline
b. A diamond flush is a
4
4
4
-card hand consisting of all diamond cards. Find the number of possible diamond flushes.
\newline
c. Find the probability of being dealt a diamond flush
\newline
a. There are a total of
270725
270725
270725
poker hands.
\newline
b. There are
\newline
19.33
19.33
19.33
0
0
0
possible diamond flushes.
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Question
13
13
13
,
11
11
11
.
5
5
5
.
15
15
15
\newline
HW score:
92.06
%
,
19.33
92.06 \%, 19.33
92.06%
,
19.33
of
\newline
Part
2
2
2
of
3
3
3
\newline
21
21
21
points
\newline
Points:
0
0
0
.
33
33
33
of
1
1
1
\newline
Save
\newline
A hand consists of
4
4
4
cards from a well-shuffled deck of
52
52
52
cards.
\newline
a. Find the total number of possible
4
4
4
-card poker hands
\newline
b. A diamond flush is a
4
4
4
-card hand consisting of all diamond cards. Find the number of possible diamond flushes.
\newline
c. Find the probability of being dealt a diamond flush
\newline
a. There are a total of
270725
270725
270725
poker hands.
\newline
b. There are
□
\square
□
possible diamond flushes.
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An apartment complex offers apartments with four different options, designated by
A
A
A
through
D
D
D
. There are an equal number of apartments with each combination of options.
\newline
\newline
A
A
A
\newline
B
B
B
\newline
C
C
C
\newline
\newline
one bedroom
\newline
two bedrooms
\newline
three bedrooms
\newline
four bedrooms
\newline
\newline
\newline
one bathroom
\newline
two bathrooms
\newline
three bathrooms
\newline
\newline
\newline
first floor
\newline
second floor
\newline
third floor
\newline
fourth floor
\newline
\newline
\newline
no special view
\newline
golf course view
\newline
lake view
\newline
parking lot view
\newline
\newline
\newline
If there is only one apartment left, what is the probability that it is precisely what a person is looking for, namely two bedrooms, three bathrooms, second floor, and a no special or lake view?
\newline
The probability is
□
\square
□
.
\newline
(Type an integer or a simplified fraction.)
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An apartment complex offers apartments with four different options, designated by A through D. There are an equal number of apartments with each combination of options.
\newline
\begin{tabular}{|c|c|c|c|}
\newline
\hline A & B & C & D \\
\newline
\hline one bedroom & one bathroom & first floor & no special view \\
\newline
\hline two bedrooms & two bathrooms & second floor & golf course view \\
\newline
\hline three bedrooms & three bathrooms & third floor & lake view \\
\newline
\hline four bedrooms & . & fourth floor & parking lot view \\
\newline
\hline
\newline
\end{tabular}
\newline
If there is only one apartment left, what is the probability that it is precisely what a person is looking for, namely two bedrooms, three bathrooms, second floor, and a no special or lake view?
\newline
The probability is
□
\square
□
.
\newline
(Type an integer or a simplified fraction.)
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Points:
0
0
0
of
1
1
1
\newline
Save
\newline
An apartment complex offers apartments with four different options, designated by A through D. There are an equal number of apartments with each combination of options.
\newline
\newline
A
\newline
B
\newline
C
\newline
D
\newline
\newline
one bedroom
\newline
one bathroom
\newline
first floor
\newline
no special view
\newline
\newline
two bedrooms
\newline
two bathrooms
\newline
second floor
\newline
golf course view
\newline
\newline
three bedrooms
\newline
three bathrooms
\newline
third floor
\newline
lake view
\newline
\newline
four bedrooms
\newline
fourth floor
\newline
parking lot view
\newline
\newline
If there is only one apartment left, what is the probability that it is precisely what a person is looking for, namely two bedrooms, three bathrooms, second floor, and a no special or lake view?
\newline
The probability is
\newline
oxed{ ext{(Type an integer or a simplified fraction.)}}.
Get tutor help
Probability with the
\newline
Question
13
13
13
,
11
11
11
.
5
5
5
.
15
15
15
\newline
HW Score:
\newline
46
46
46
.
03
03
03
\%,
9
9
9
.
67
67
67
of
21
21
21
\newline
Part
1
1
1
of
3
3
3
\newline
points
\newline
Points:
0
0
0
of
1
1
1
\newline
Save
\newline
Question list
\newline
anunu....
\newline
Question
12
12
12
\newline
Question
13
13
13
\newline
Question
14
14
14
\newline
Question
15
15
15
\newline
A hand consists of
5
5
5
cards from a well-shuffled deck of
52
52
52
cards.
\newline
a. Find the total number of possible
5
5
5
-card poker hands.
\newline
b. A heart flush is a
5
5
5
-card hand consisting of all heart cards. Find the number of possible heart flushes.
\newline
c. Find the probability of being dealt a heart flush.
\newline
a. There are a total of
\newline
□
\square
□
poker hands.
Get tutor help
Probability with the
\newline
Question
13
13
13
,
11
11
11
.
5
5
5
.
15
15
15
\newline
HW Score:
46.03
%
,
9.67
46.03 \%, 9.67
46.03%
,
9.67
of
21
21
21
\newline
Part
1
1
1
of
3
3
3
\newline
points
\newline
Points:
0
0
0
of
1
1
1
\newline
Save
\newline
Question list
\newline
-nuvu.....
\newline
Question
12
12
12
\newline
Question
13
13
13
\newline
Question
14
14
14
\newline
Question
15
15
15
\newline
A hand consists of
5
5
5
cards from a well-shuffled deck of
52
52
52
cards.
\newline
a. Find the total number of possible
5
5
5
-card poker hands.
\newline
b. A heart flush is a
5
5
5
-card hand consisting of all heart cards. Find the number of possible heart flushes.
\newline
c. Find the probability of being dealt a heart flush.
\newline
a. There are a total of
□
\square
□
poker hands.
Get tutor help
In a lottery, the top cash prize was
$
610
\$610
$610
million, going to three lucky winners. Players pick four different numbers from
1
1
1
to
56
56
56
and one number from
1
1
1
to
43
43
43
A player wins a minimum award of
$
300
\$300
$300
by correctly matching two numbers drawn from the white balls (
1
1
1
through
56
56
56
) and matching the number on the gold ball (
1
1
1
through
43
43
43
) What is the probability of winning the minimum award? The probability of winning the minimum award is ◻ (Type an integer or a simplified fraction )
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Probability with the
\newline
Question
10
10
10
,
11
11
11
.
5
5
5
.
9
9
9
\newline
points
\newline
Fundamental Countin
\newline
Points:
0
0
0
of
1
1
1
\newline
Save
\newline
Question list
\newline
Question
6
6
6
\newline
Question
7
7
7
\newline
x
/
3
x / 3
x
/3
Question
8
8
8
\newline
* Question
9
9
9
\newline
In a lottery, the top cash prize was
$
610
\$ 610
$610
million, going to three lucky winners. Players pick four different numbers from
1
1
1
to
56
56
56
and one number from
1
1
1
to
43
43
43
\newline
A player wins a minimum award of
$
300
\$ 300
$300
by correctly matching two numbers drawn from the white balls (
1
1
1
through
56
56
56
) and matching the number on the gold ball (
1
1
1
through
43
43
43
) What is the probability of winning the minimum award?
\newline
The probability of winning the minimum award is
□
\square
□
\newline
(Type an integer or a simplified fraction.)
Get tutor help
Probability with the
\newline
Fundamental Countin
\newline
Question
13
13
13
,
11
11
11
.
5
5
5
.
15
15
15
\newline
HW Score:
46.03
%
,
9.67
46.03 \%, 9.67
46.03%
,
9.67
of
21
21
21
\newline
Part
1
1
1
of
3
3
3
\newline
points
\newline
Points:
0
0
0
of
1
1
1
\newline
Save
\newline
Question list
\newline
( Question
9
9
9
\newline
( Question
10
10
10
\newline
Question
11
11
11
\newline
A hand consists of
5
5
5
cards from a well-shuffled deck of
52
52
52
cards.
\newline
a. Find the total number of possible
5
5
5
-card poker hands.
\newline
b. A heart flush is a
5
5
5
-card hand consisting of all heart cards. Find the number of possible heart flushes.
\newline
c. Find the probability of being dealt a heart flush.
\newline
a. There are a total of
□
\square
□
poker hands.
Get tutor help
A hand consists of
4
4
4
cards from a well-shuffled deck of
52
52
52
cards
\newline
a. Find the total number of possible
4
4
4
-card poker hands
\newline
b. A diamond flush is a
4
4
4
-card hand consisting of all diamond cards. Find the number of possible diamond flushes.
\newline
c. Find the probability of being dealt a diamond flush.
\newline
a. There are a total of
□
\square
□
poker hands.
Get tutor help
In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (
1
1
1
through
45
45
45
) and matching the number on the gold ball (
1
1
1
through
35
35
35
). If one ticket is purchased, what is the probability of winning the jackpot?
\newline
The probability of winning the jackpot with one ticket is
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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
3
3
3
-year security,
1
1
1
year from now?
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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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