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Suppose you drop a die at random on the rectangular region shown in Fig. 15.6. What is the probability that it will land inside the circle with diameter 1m?

First, calculate the area of the rectangle and the area of the circle. Here, the area of the rectangle is the possible outcome and the area of the circle will be the favourable outcome.

So, the area of the rectangle = (3 × 2) m2 = 6 m2

and,

The area of the circle $$= \ \pi r^2 \ = \ \pi ( \frac{1}{2})^2 \ = \ \frac{ \pi}{4} \ = \ 0.78$$

$$\therefore$$ The probability that die will land inside the circle $$= \ \frac{ \frac{ \pi}{4}}{6} \ = \ \frac{\pi}{24} \ = \ 0.13$$