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Question

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

Area of the circle = $$\pi { r }^{ 2 }=\dfrac{\pi ({ 1) }^{ 2 }}{4}=\dfrac{\pi}{4} $$ sq m.
Area of the rectangle $$= 3 \times 2 = 6$$ sq m.
$$P($$Die will land in the circle$$)= \dfrac{\text{Area of circle}}{\text{Area of rectangle}}= \dfrac{\pi}{24}$$

$$P($$Die will land in the circle$$) = \dfrac{\pi}{24}$$

Mathematics
RS Agarwal
Standard X

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