Question

On a used car lot, $50\%$ of the vehicles are cars, $\frac{3}{4}$ of which have 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?

• A. $\frac{1}{8}$
• B. $\frac{1}{6}$
• C. $\frac{1}{4}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{1}{8}$

Let the total number of vehicles be $N$.

The total number of cars will be $\frac{N}{2}$.

The total number of cars with automatic transmission will be $=\frac{3}{4}\times \frac{N}{2}=\frac{3N}{8}$.

The total number of cars having leather interiors and automatic transmission is $=\frac{1}{3}\times \frac{3N}{8}=\frac{N}{8}$.
Hence, the required probability is
$=\frac{\frac{N}{8}}{N}$ $=\frac{1}{8}$