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Precalculus
Find probabilities using the addition rule
Question
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Show Examples
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In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student chosen randomly from the class does not have a sister?
\newline
\begin{tabular}{|c|c|c|}
\newline
\hline & Has a brother & Does not have a brother \\
\newline
\hline Has a sister &
4
4
4
&
5
5
5
\\
\newline
\hline Does not have a sister &
8
8
8
&
12
12
12
\\
\newline
\hline
\newline
\end{tabular}
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Answer Attempt
2
2
2
out of
2
2
2
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Question
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Show Examples
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In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument?
\newline
\begin{tabular}{|c|c|c|}
\newline
\hline & \begin{tabular}{c}
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Plays an \\
\newline
instrument
\newline
\end{tabular} & \begin{tabular}{c}
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Does not play \\
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an instrument
\newline
\end{tabular} \\
\newline
\hline \begin{tabular}{c}
\newline
Plays a \\
\newline
sport
\newline
\end{tabular} &
2
2
2
&
4
4
4
\\
\newline
\hline
\newline
\end{tabular}
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4
4
4
.
6
6
6
.
3
3
3
Test (CST): Undoing Functions and Moving Them Around
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Question
1
1
1
of
25
25
25
\newline
Suppose that
g
(
x
)
=
f
(
x
)
−
3
g(x)=f(x)-3
g
(
x
)
=
f
(
x
)
−
3
. Which statement best compares the graph of
g
(
x
)
g(x)
g
(
x
)
with the graph of
f
(
x
)
f(x)
f
(
x
)
?
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A. The graph of
g
(
x
)
g(x)
g
(
x
)
is vertically stretched by a factor of
3
3
3
.
\newline
B. The graph of
g
(
x
)
g(x)
g
(
x
)
is shifted
3
3
3
units to the left.
\newline
C. The graph of
g
(
x
)
g(x)
g
(
x
)
is shifted
3
3
3
units down.
\newline
D. The graph of
g
(
x
)
g(x)
g
(
x
)
is shifted
3
3
3
units up.
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Solve using the Negative Binomial Distribution and/or Geometric Distribution! Qin Er Shi was the second Emperor of the Qin dynasty and the son of Qin Shi Huang, the founder of the Great Wall of China. Since Qin Er Shi was very weak, Prime Minister Zhao Gao had the opportunity to dominate the running of the Qin dynasty government. Zhao Gao heard reports from his followers that
60
%
60\%
60%
of the Chinese people were no longer loyal to Qin Er Shi's leadership while the remainder (
40
%
40\%
40%
) were still loyal. To ensure that, Zhao Gao planned to disguise himself as a commoner and travel for a day in the city of Xianyang (the capital of China at that time) where he would extract information from everyone he met whether they were loyal or not to the Emperor. A dilemma arises considering that Zhao Gao is no longer young and the chance of Zhao Gao walking more than
10.25
km
10.25\,\text{km}
10.25
km
in one day is
50
%
50\%
50%
. It is known that the distance per day that Zhao Gao can cover is Gaussian distributed with a variance of
6.25
km
6.25\,\text{km}
6.25
km
. If it is assumed that the level of loyalty of the people of Xianyang city to the Emperor is no different from the level of loyalty of the Chinese people in general, determine: a) The probability that Zhao Gao can find three people who are NOT loyal to the Emperor after Zhao Gao investigates at most five people! b) If the probability that Zhao Gao can cover a distance of more than
B
km
B\,\text{km}
B
km
in a day's journey is
39
%
39\%
39%
, then determine
B
B
B
! c) Chances are that Zhao Gao had to investigate six people to find the first person who was loyal to the Emperor! It is known that
Z
Z
Z
is the number of officials who dare to tell the truth and say that the animal is a deer. d) Determine the appropriate type of distribution to describe
Z
Z
Z
and explain your motivation. e) Calculate the probability that the majority of officials dare to tell the truth. f) Calculate the probability that the majority of officials continue to obey Zhao Gao.
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2
2
2
) On a shelf there are
60
60
60
novels and
20
20
20
poetry books. What is the probability that Person A chooses a novel and walks away with it and then Person B walks up shortly after and picks another novel?
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The accompanying table shows the results of a survey in which
250
250
250
male and
250
250
250
female workers ages
25
25
25
to
64
64
64
were asked if they contribute to a retirement savings plan at work. Compl and (b) below.
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Click the icon to view the survey results.
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(a) Find the probability that a randomly selected worker contributes to a retirement savings plan at work, given that the worker is male.
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The probability that a randomly selected worker contributes to e retirement savings plan at work, given that the worker is male, is
\newline
oxed{ ext{◻}}.
\newline
(Round to three decimal places as needed.)
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(b) Find the probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work.
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The probability that a randomly selected worker is female, given that the worker contributes to a retirement savings plan at work, is
\newline
oxed{ ext{◻}}.
\newline
(Round to three decimal places as needed.)
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Survey Results
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\newline
\newline
Contribute
\newline
Do not contribute
\newline
Total
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\newline
Male
\newline
123
123
123
\newline
127
127
127
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250
250
250
\newline
\newline
Female
\newline
155
155
155
\newline
250
250
250
0
0
0
\newline
250
250
250
\newline
\newline
Total
\newline
250
250
250
2
2
2
\newline
250
250
250
3
3
3
\newline
250
250
250
4
4
4
\newline
\newline
Print
\newline
Done
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The cost of a sleeping bag has been discounted by
$
22
\$ 22
$22
, so that the sale price of the bag is
552
552
552
Find the onginat price of the sleeping bag. p, by solving the equation
p
−
22
=
52
p-22=52
p
−
22
=
52
.
\newline
The original price of the sleeping bag was
$
□
\$ \square
$
□
.
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Jacci has a fair coin and a wooden cube. On the cube, there are two faces colored green, two faces colored blue, and two faces colored red. Mary flips the coin and tosses the cube. What is the probability of getting both a tail on the toss of the coin and a green face on the roll of the cube?
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