For a special report in the Cedar Rapids, IA, Gazette, reporters used a radar gun to
check the speeds of 1,239 drivers in two counties. They were shocked (!) to discover
that some drivers were driving at a speed greater than the posted limits. They
reported the following information in their story: $$\begin{array}{l}
\text { Speeding data for cities in Linn and Johnson Counties }\
\begin{array} { | l | c | c | c | c | }
\hline \text { City } & \begin{array} { l }
\text { City } \
\text { Speed } \
\text { Limit }
\end{array} & \begin{array} { l }
\text { Drivers } \
\text { Observed }
\end{array} & \begin{array} { l }
\text { Over } \
\text { Limit }
\end{array} & \begin{array} { l }
\text { \%Over } \
\text { Limit }
\end{array} \
\hline \text { Cedar Rapids } & 25 & 241 & 233 & 96.7 \
\text { Iowa City } & 35 & 292 & 124 & 42.5 \
\text { Iowa City } & 20 & 203 & 203 & 100.0 \
\text { Marion } & 30 & 329 & 268 & 81.5 \
\text { Coralville } & 25 & 174 & 161 & 92.5 \
\hline
\end{array}
\end{array}$$ Suppose that one of these drivers is selected at random. Define the following events:
F = the event that a randomly selected driver was in the fast lane (speed limit
above 25 mph)
S = the event that a randomly selected driver is speeding.
a) The table below shows the possible combinations of F and S. For each
combination, calculate the probability that the combination would be observed for
a randomly selected driver. Enter these probabilities into the corresponding cell in
the table. $$\begin{array} { | l | c | c | }
\hline & \begin{array} { c }
\text { Speed Limit } \
25 \mathrm { mph } \
\text { (Fast lane) }
\end{array} & \begin{array} { c }
\text { Speed Limit } \
\text { 25mph or less } \
\text { (Slow lane) }
\end{array} \
\hline \text { Driver speeding } & & \
\hline \text { Driver not speeding } & & \
\hline
\end{array}$$ $$\text { b) Using the information in your table from part (a), calculate } P ( F \cup S ) \text {. }$$ $$\text { c) Using the information in your table from part (a), calculate } P \left( S ^ { C } \right)$$

Question

For a special report in the Cedar Rapids, IA, Gazette, reporters used a radar gun to
check the speeds of 1,239 drivers in two counties. They were shocked (!) to discover
that some drivers were driving at a speed greater than the posted limits. They
reported the following information in their story: $$\begin{array}{l}
\text { Speeding data for cities in Linn and Johnson Counties }\
\begin{array} { | l | c | c | c | c | } 
\hline \text { City } & \begin{array} { l } 
\text { City } \
\text { Speed } \
\text { Limit }
\end{array} & \begin{array} { l } 
\text { Drivers } \
\text { Observed }
\end{array} & \begin{array} { l } 
\text { Over } \
\text { Limit }
\end{array} & \begin{array} { l } 
\text { \%Over } \
\text { Limit }
\end{array} \
\hline \text { Cedar Rapids } & 25 & 241 & 233 & 96.7 \
\text { Iowa City } & 35 & 292 & 124 & 42.5 \
\text { Iowa City } & 20 & 203 & 203 & 100.0 \
\text { Marion } & 30 & 329 & 268 & 81.5 \
\text { Coralville } & 25 & 174 & 161 & 92.5 \
\hline
\end{array}
\end{array}$$ Suppose that one of these drivers is selected at random. Define the following events:
F = the event that a randomly selected driver was in the fast lane (speed limit
above 25 mph)
S = the event that a randomly selected driver is speeding.
a) The table below shows the possible combinations of F and S. For each
combination, calculate the probability that the combination would be observed for
a randomly selected driver. Enter these probabilities into the corresponding cell in
the table. $$\begin{array} { | l | c | c | } 
\hline & \begin{array} { c } 
\text { Speed Limit } \
> 25 \mathrm { mph } \
\text { (Fast lane) }
\end{array} & \begin{array} { c } 
\text { Speed Limit } \
\text { 25mph or less } \
\text { (Slow lane) }
\end{array} \
\hline \text { Driver speeding } & & \
\hline \text { Driver not speeding } & & \
\hline
\end{array}$$ $$\text { b) Using the information in your table from part (a), calculate } P ( F \cup S ) \text {. }$$ $$\text { c) Using the information in your table from part (a), calculate } P \left( S ^ { C } \right)$$

Quizplus · Accepted Answer

The Answer of For a special report in the Cedar Rapids, IA, Gazette, reporters used a radar gun to
check the speeds of 1,239 drivers in two counties. They were shocked (!) to discover
that some drivers were driving at a speed greater than the posted limits. They
reported the following information in their story: $$\begin{array}{l}
\text { Speeding data for cities in Linn and Johnson Counties }\
\begin{array} { | l | c | c | c | c | } 
\hline \text { City } & \begin{array} { l } 
\text { City } \
\text { Speed } \
\text { Limit }
\end{array} & \begin{array} { l } 
\text { Drivers } \
\text { Observed }
\end{array} & \begin{array} { l } 
\text { Over } \
\text { Limit }
\end{array} & \begin{array} { l } 
\text { \%Over } \
\text { Limit }
\end{array} \
\hline \text { Cedar Rapids } & 25 & 241 & 233 & 96.7 \
\text { Iowa City } & 35 & 292 & 124 & 42.5 \
\text { Iowa City } & 20 & 203 & 203 & 100.0 \
\text { Marion } & 30 & 329 & 268 & 81.5 \
\text { Coralville } & 25 & 174 & 161 & 92.5 \
\hline
\end{array}
\end{array}$$ Suppose that one of these drivers is selected at random. Define the following events:
F = the event that a randomly selected driver was in the fast lane (speed limit
above 25 mph)
S = the event that a randomly selected driver is speeding.
a) The table below shows the possible combinations of F and S. For each
combination, calculate the probability that the combination would be observed for
a randomly selected driver. Enter these probabilities into the corresponding cell in
the table. $$\begin{array} { | l | c | c | } 
\hline & \begin{array} { c } 
\text { Speed Limit } \
> 25 \mathrm { mph } \
\text { (Fast lane) }
\end{array} & \begin{array} { c } 
\text { Speed Limit } \
\text { 25mph or less } \
\text { (Slow lane) }
\end{array} \
\hline \text { Driver speeding } & & \
\hline \text { Driver not speeding } & & \
\hline
\end{array}$$ $$\text { b) Using the information in your table from part (a), calculate } P ( F \cup S ) \text {. }$$ $$\text { c) Using the information in your table from part (a), calculate } P \left( S ^ { C } \right)$$

For a Special Report in the Cedar Rapids, IA, Gazette