Question

7. Everyone working in a Florida office building was tested for Covid-19 when the building reopened for business on August \( 1^{\text {st. }} \). Only those with negative tests were allowed to return to work. \( 45 \% \) of the office building occupants had been vaccinated \( [\mathrm{P}(\mathrm{V})=.45 \) ]. All of the employees were tested again on October \( 1^{\text {st }} \). Of those who were vaccinated, \( 2 \% \) tested positive. Of those who weren't vaccinated, \( 18 \% \) tested positive.. Let, \( \mathbf{V}= \) vaccinated, \( \quad \mathbf{N}= \) Not Vaccinated, \( \quad \mathrm{C}= \) has/had Covid by October, \( \mathrm{S}= \) no Covid by October Note that \( \mathrm{V} \) and \( \mathrm{N} \) are complementary events. \( \mathrm{C} \) and \( \mathrm{S} \) are complementary events. From the given information: \( \quad \mathrm{P}(\mathrm{V})=.45 \quad \mathrm{P}(\mathrm{C} \mid \mathrm{V})=.02 \quad \mathrm{P}(\mathrm{C} \mid \mathrm{N})=.18 \) You may wish to make a tree diagram on another sheet of paper to help find the proportions of employees for each cell in the table below. a) Fill in the proportions in the table. \begin{tabular}{|l|l|l|l|} \hline & \begin{tabular}{l} \( \mathrm{V}= \) \\ vaccinated \end{tabular} & \begin{tabular}{l} \( \mathrm{N}= \) not \\ vaccinated \end{tabular} & totals \\ \hline \begin{tabular}{l} \( \mathrm{C}= \) caught \\ Covid-19 \end{tabular} & & & \\ \hline \begin{tabular}{l} \( \mathrm{S}= \) didn't \\ get Covid-19 \end{tabular} & & & \\ \hline & & & 1.000 \\ \hline totals & & & \\ \hline \end{tabular} Show your answers rounded to four decimal places if rounding is necessary. b) What proportion of the employees got Covid in August or September? b) \( \qquad \) c) What proportion of those who got Covid were not vaccinated? c) \( \qquad \) d) Are being vaccinated and getting Covid independent? EXPLAIN how you reach this conclusion. I'm looking for an explanation that demonstrates that you know what independent means. e) Are being vaccinated and getting Covid mutually exclusive? EXPLAIN how you reach this conclusion. I'm looking for an explanation that demonstrates that you know what mutually exclusive means.

          7. Everyone working in a Florida office building was tested for Covid-19 when the building reopened for business on August \( 1^{\text {st. }} \). Only those with negative tests were allowed to return to work. \( 45 \% \) of the office building occupants had been vaccinated \( [\mathrm{P}(\mathrm{V})=.45 \) ].

All of the employees were tested again on October \( 1^{\text {st }} \).
Of those who were vaccinated, \( 2 \% \) tested positive. Of those who weren't vaccinated, \( 18 \% \) tested positive..
Let, \( \mathbf{V}= \) vaccinated, \( \quad \mathbf{N}= \) Not Vaccinated, \( \quad \mathrm{C}= \) has/had Covid by October, \( \mathrm{S}= \) no Covid by October
Note that \( \mathrm{V} \) and \( \mathrm{N} \) are complementary events. \( \mathrm{C} \) and \( \mathrm{S} \) are complementary events.
From the given information: \( \quad \mathrm{P}(\mathrm{V})=.45 \quad \mathrm{P}(\mathrm{C} \mid \mathrm{V})=.02 \quad \mathrm{P}(\mathrm{C} \mid \mathrm{N})=.18 \)
You may wish to make a tree diagram on another sheet of paper to help find the proportions of employees for each cell in the table below.
a) Fill in the proportions in the table.
\begin{tabular}{|l|l|l|l|}
\hline & \begin{tabular}{l}
\( \mathrm{V}= \) \\
vaccinated
\end{tabular} & \begin{tabular}{l}
\( \mathrm{N}= \) not \\
vaccinated
\end{tabular} & totals \\
\hline \begin{tabular}{l}
\( \mathrm{C}= \) caught \\
Covid-19
\end{tabular} & & & \\
\hline \begin{tabular}{l}
\( \mathrm{S}= \) didn't \\
get Covid-19
\end{tabular} & & & \\
\hline & & & 1.000 \\
\hline totals & & & \\
\hline
\end{tabular}

Show your answers rounded to four decimal places if rounding is necessary.
b) What proportion of the employees got Covid in August or September?
b) \( \qquad \)
c) What proportion of those who got Covid were not vaccinated?
c) \( \qquad \)
d) Are being vaccinated and getting Covid independent? EXPLAIN how you reach this conclusion. I'm looking for an explanation that demonstrates that you know what independent means.
e) Are being vaccinated and getting Covid mutually exclusive? EXPLAIN how you reach this conclusion. I'm looking for an explanation that demonstrates that you know what mutually exclusive means.

7. Everyone working in a Florida office building was tested for Covid-19 when the building reopened for business on August 1^st.. Only those with negative tests were allowed to return to work. 45 % of the office building occupants had been vaccinated [P(V)=.45 ].

All of the employees were tested again on October 1^st.
Of those who were vaccinated, 2 % tested positive. Of those who weren't vaccinated, 18 % tested positive..
Let, 𝐕= vaccinated, 𝐍= Not Vaccinated, C= has/had Covid by October, S= no Covid by October
Note that V and N are complementary events. C and S are complementary events.
From the given information: P(V)=.45 P(C|V)=.02 P(C|N)=.18
You may wish to make a tree diagram on another sheet of paper to help find the proportions of employees for each cell in the table below.
a) Fill in the proportions in the table.

V=

vaccinated

N= not

vaccinated
totals

C= caught

Covid-19

S= didn't

get Covid-19

1.000

totals

Show your answers rounded to four decimal places if rounding is necessary.
b) What proportion of the employees got Covid in August or September?
b)
c) What proportion of those who got Covid were not vaccinated?
c)
d) Are being vaccinated and getting Covid independent? EXPLAIN how you reach this conclusion. I'm looking for an explanation that demonstrates that you know what independent means.
e) Are being vaccinated and getting Covid mutually exclusive? EXPLAIN how you reach this conclusion. I'm looking for an explanation that demonstrates that you know what mutually exclusive means.

Added by Consuelo C.

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