Question

A die is dropped at random on the rectangular region of sides $3m\times 2m$. What is the probability that it will land inside a circle(lying inside the rectangle) with diameter 1 m?

• A. $\frac{\pi }{48}$
• B. $\frac{\pi }{24}$
• C. $\frac{\pi }{36}$
• D. $\frac{\pi }{12}$

Answer 1

The correct option is B $\frac{\pi }{24}$

Area of rectangular region $=3m\times 2m=6m^2$

As, diameter = 1 m, radius will be $\frac{1}{2}$ m.

Area of circle $=\pi r^2=\frac{\pi }{4}$

Probability die will land inside the circle = $\frac{\text{Area of circle}}{\text{Area of rectangular region}}$

Probability that die will land inside the circle $=\frac{\pi }{4}÷6=\frac{\pi }{24}$