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

Explanation

We use the concepts of areas of circles and squares and also the basic concepts of probability.
Length of rectangular region = `3` m
Breadth of rectangular region = `2` m
Area of rectangular region = Length × Breadth
= `3 × 2`
= `6 m^2`
Diameter of circular region = `1` m
Radius of circular region = `1/2` m
Area of circular region = `pi r^2`
= `pi × (1/2)^2`
= `pi/4`
The probability that it will land inside the circle = (Number of possible outcomes)/(Total number of favorable outcomes)
= Area of circular region/Area of the rectangular region
= `(pi/4)/6`
= `pi/24`
The probability that it will land inside the circle is `pi/24`