Question

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 1m?

Answer 1

Area of rectangle = l × b = 3 × 2 = 6 m²

Area of circle (of diameter 1 m)  = `pir^2= pi((1)/2)^2 m^2= pi/4 m^2`

∴ Probability that the die will fall inside the

Cicle = `"Area of the favourable region"/ "Area of the whole region"`

= `"Area of the circle"/"Area of the rectangle"`

`= (pi/4)/6 = pi/4 xx 1/6 = pi/24`

P (die will land inside the circle) = `(pi/4)/6= pi/24`