To find the fraction of cars in the lot that are both gray and electrically powered, we can follow these steps:
- Identify the fraction of gray cars: According to the problem, \( \frac{2}{5} \) of the cars are gray.
- Identify the fraction of gray cars that are electrically powered: We know that \( \frac{1}{3} \) of the gray cars are electrically powered.
Now, we will calculate the fraction of the total cars that are both gray and electrically powered by multiplying the two fractions:
\[ \text{Fraction of gray and electrically powered cars} = \text{Fraction of gray cars} \times \text{Fraction of gray cars that are electrically powered} \]
\[ = \frac{2}{5} \times \frac{1}{3} \]
Next, we multiply the numerators and denominators:
\[ = \frac{2 \times 1}{5 \times 3} = \frac{2}{15} \]
Thus, the fraction of the cars on the lot that are both gray and electrically powered is \(\frac{2}{15}\).