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

Suppose you drop a die at random on the rectangular region shown. What is the probability that it will land inside the circle with diameter 1 m? NCERT Class 10 Mathematics CBSE Solutions.

Probability

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Answer

Length of rectangular region = 3 m

Breadth of rectangular region = 2 m

Area of rectangular region = Length × Breadth

= 3 × 2 = 6 m2.

Diameter of circular region = 1 m

Radius of circular region (r) = 12\dfrac{1}{2} m

Area of circular region = πr2

= π × (12)2\Big(\dfrac{1}{2}\Big)^2

= π4\dfrac{π}{4} m2.

The probability that it will land inside the circle

= Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

= Area of circular regionArea of the rectangular region\dfrac{\text{Area of circular region}}{\text{Area of the rectangular region}}

= π46=π24\dfrac{\dfrac{π}{4}}{6} = \dfrac{π}{24}.

Hence, the probability that die will land inside the circle is π24\dfrac{π}{24}.

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