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

Step 1: Observe the given figure and find the areas of the given shapes.
GIVEN: length = 3m
breadth = 2m
Area of the rectangular region = length * breadth = 3 * 2 = 6
Diameter = 1 m
Radius = \frac{1}{2}
Area of the circle = \pi r^2
= \pi (\frac{1}{2})^2
= \frac{\pi}{4} m^2
Step 2: Calculate the probability that the die will land inside the circle
Total outcomes = Area of the rectangular region = 6
Favorable outcomes = Area of the circle = \frac{\pi}{4}
P(die will land inside the circle) = \frac{Favorable\ out\ comes}{Total\ outcomes}
= \frac{ \frac{\pi}{4}}{6}
= \frac{\pi}{4*6}
= \frac{\pi}{24}
Hence, probability = \frac{\pi}{24}