Question

5 multiple choice 1 point
on a used vehicle lot, 50 percent of the vehicles are cars, \\( \frac { 3 } { 4 } \\) of which have automatic transmissions. of the cars with automatic transmissions, \\( \frac { 1 } { 3 } \\) have leather interiors. if a vehicle is chosen from the lot at random, what is the probability that it will be a car with an automatic transmission and a leather interior?
\\( \bigcirc \frac { 1 } { 6 } \\)
\\( \bigcirc \frac { 1 } { 4 } \\)
\\( \bigcirc \frac { 1 } { 8 } \\)
\\( \bigcirc \frac { 1 } { 3 } \\)

Explanation:

Step1: Calculate the proportion of cars

Let the total number of vehicles be \(1\). Since \(50\%=\frac{1}{2}\) of the vehicles are cars.

Step2: Calculate the proportion of cars with automatic transmissions

Of the cars, \(\frac{3}{4}\) have automatic transmissions. So the proportion of cars with automatic transmissions is \(\frac{1}{2}\times\frac{3}{4}\).

Step3: Calculate the proportion of cars with automatic transmissions and leather interiors

Of the cars with automatic transmissions, \(\frac{1}{3}\) have leather interiors. So the proportion is \(\frac{1}{2}\times\frac{3}{4}\times\frac{1}{3}\).

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Answer:

\(\frac{1}{8}\) (corresponding to the third option)