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  • A point is selected at random from the interior of a circle. The probability that the point is closer to the centre than the boundary of the circle isOption: 1</

A point is selected at random from the interior of a circle. The probability that the point is closer to the centre than the boundary of the circle is

Option: 1

\frac{3}{4}


Option: 2

\frac{1}{2}


Option: 3

\frac{1}{4}


Option: 4

None of these


Answers (1)

best_answer

\mathrm{n(S)=} the area of the circle of radius r

\mathrm{n(E)=} the area of the circle of radius \mathrm{\frac{r}{2}}.

\therefore  the required probability

\mathrm{=\frac{n(E)}{n(S)}=\frac{\pi \cdot\left(\frac{r}{2}\right)^2}{\pi r^2}=\frac{1}{4} . }


 

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Rishi

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