Question

Question 20
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

Total area of the given figure (rectangle) = 3 $\times$ 2 = 6 m${}^2$
And Area of circle (favourable area)= $\pi$r${}^2$ = $\pi {\left(\frac{1}{2}\right)}^2=\frac{\pi }{4}{m}^2$

Hence, P (die will land inside the circle)
$=\frac{Favourablearea}{Totalarea}=\frac{\pi /4}{6}=\frac{\pi }{24}$