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

Area of rectangle = $3 \times 2 = 6 \text{ m}^2$ .

Diameter of circle = 1 m

So, radius of circle = 0.5 m.

$$\text{Area of circle} = \pi r^2 = \pi \times (0.5)^2 = \frac{\pi}{4} \text{ m}^2.$$

$$P(\text{lands inside circle}) = \frac{\frac{\pi}{4}}{6} = \frac{\pi}{24}.$$