The manager of a used car lot took inventory of the automobiles on his lot and constructed the following tablebased on the age of his car and its make (foreign or domestic). $$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Age of Car (in years) }\
\begin{array} { r | c c c c | c }
{ \text { Make } } & 0 - 2 & 3 - 5 & 6 - 10 & \text { over } 10 & \text { Total } \
\hline \text { Foreign } & 42 & 24 & 13 & 21 & 100 \
\text { Domestic } & 36 & 23 & 11 & 30 & 100 \
\hline \text { Total } & 78 & 47 & 24 & 51 & 200
\end{array}
\end{array}$$ A car was randomly selected from the lot. Given that the car selected is older than two years old, find theprobability that it is not a foreign car.
A) $\frac { 32 } { 61 }$
B) $\frac { 29 } { 61 }$
C) $\frac { 16 } { 25 }$
D) $\frac { 29 } { 50 }$
Find the indicated probability. Give your answer as a decimal rounded to the nearest thousandth.

Question

The manager of a used car lot took inventory of the automobiles on his lot and constructed the following tablebased on the age of his car and its make (foreign or domestic). $$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Age of Car (in years) }\
\begin{array} { r | c c c c | c } 
{ \text { Make } } & 0 - 2 & 3 - 5 & 6 - 10 & \text { over } 10 & \text { Total } \
\hline \text { Foreign } & 42 & 24 & 13 & 21 & 100 \
\text { Domestic } & 36 & 23 & 11 & 30 & 100 \
\hline \text { Total } & 78 & 47 & 24 & 51 & 200
\end{array}
\end{array}$$ A car was randomly selected from the lot. Given that the car selected is older than two years old, find theprobability that it is not a foreign car. 
A) $\frac { 32 } { 61 }$
B) $\frac { 29 } { 61 }$
C) $\frac { 16 } { 25 }$
D) $\frac { 29 } { 50 }$ 
Find the indicated probability. Give your answer as a decimal rounded to the nearest thousandth.

Quizplus · Accepted Answer

The probability that the car selected is older than two years old is:$$P(Age > 2) = \frac{47 + 24 + 51}{200} = \frac{122}{200} = 0.61$$The probability that the car selected is not a foreign car is:$$P(Not\ Foreign) = \frac{100}{200} = 0.5$$Therefore, the probability that the car selected is older than two years old and not a foreign car is:$$P(Age > 2 \cap Not\ Foreign) = P(Age > 2) \times P(Not\ Foreign) = 0.61 \times 0.5 = 0.305$$Therefore, the probability that the car selected is older than two years old and not a foreign car is 0.305, which is closest to choice A, $\frac { 32 } { 61 }$.

The Manager of a Used Car Lot Took Inventory of the Automobiles