Suppose you drop a die at random on the rectangular region shown in the figure. What is the probability that it will land inside the circle with diameter $1 \, m$?

(N/A) The area of the rectangular region is given by $Area = \text{length} \times \text{breadth} = 3 \, m \times 2 \, m = 6 \, m^2$.
The diameter of the circle is $1 \, m$, so its radius $r = \frac{1}{2} \, m$.
The area of the circle is given by $Area = \pi r^2 = \pi \left(\frac{1}{2}\right)^2 = \frac{\pi}{4} \, m^2$.
The probability that the die will land inside the circle is the ratio of the area of the circle to the total area of the rectangle:
$P(\text{landing inside the circle}) = \frac{\text{Area of circle}}{\text{Area of rectangle}} = \frac{\frac{\pi}{4}}{6} = \frac{\pi}{24}$.