Question

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

Answer 1

Area of the circle = $\pi r^2=\frac{\pi ({1)}^2}{4}=\frac{\pi }{4}$ sq m.

Area of the rectangle $=3\times 2=6$ sq m.

$P($Die will land in the circle$)=\frac{\text{Area of circle}}{\text{Area of rectangle}}=\frac{\pi }{24}$

$P($Die will land in the circle$)=\frac{\pi }{24}$