Question

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

Answer 1

Area of rectangle $= l × b = 3 × 2 = 6 m^2$
Area of circle (of diameter 1 m) $=\pi r^2 = \pi (\frac{1}{2})^2 m^2 = \frac{\pi}{4} m^2 = 0.78$

P (die will land inside the circle) $=\left[\frac{(\frac{\pi}{4})}{6}\right] = \frac{\pi}{24}\ \text{ or},\frac{ 0.78}{6} = 0.13$