A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a dice, very small in size, is dropped on the rectangular paper without seeing towards it. If the dice falls and lands on the paper only, find the probability that it will fall and land :

(i) inside the circle.

(ii) outside the circle.

Diameter of circle drawn = 20 cm

Radius = $\dfrac{\text{Diameter}}{2} = \dfrac{20}{2}$ = 10 cm.

Area of circle = πr²

$= \dfrac{22}{7} \times 10 \times 10 \\[1em] = \dfrac{2200}{7} \text{ cm}^2.$

Length of rectangular piece = 40 cm

Width of rectangular piece = 30 cm

Area of rectangular piece (Total possible outcome) = 40 × 30 = 1200 cm²

(i) No. of favourable outcome for dice landing inside circle = Area of circle = $\dfrac{2200}{7}$ cm².

P(dice lands inside circle)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{\dfrac{2200}{7}}{1200} = \dfrac{2200}{8400} = \dfrac{11}{42}$.

Hence, the probability that dice lands inside the circle = $\dfrac{11}{42}$.

(ii) P(dice lands inside circle) + P(dice lands outside the circle) = 1

P(dice lands outside circle) = 1 - P(dice lands inside the circle)

= 1 - $\dfrac{11}{42}$

= $\dfrac{42 - 11}{42}$

= $\dfrac{31}{42}$.

Hence, the probability that dice lands outside the circle = $\dfrac{31}{42}$.