Question

What is the probability that a die thrown randomly on the rectangular region will land inside the circle with diameter 1 m?

• A. $\frac{\pi }{24}$
• B. $\frac{1}{24}$
• C. $\frac{21}{\pi }$
• D. 0

Answer 1

The correct option is A

$\frac{\pi }{24}$

Total area of the given figure (rectangle) = 3 $\times$ 2 = 6 m${}^2$
And Area of circle = $\pi$r${}^2$ = $\pi {\left(\frac{1}{2}\right)}^2=\frac{\pi }{4}{m}^2$
Hence, P (die will land inside the circle) = $\frac{\pi /4}{6}=\frac{\pi }{24}$