Question

A point is selected randomly from the inside of the circle. The probability that point is closer to the centre then the boundary of the circle is

• A. $\frac{4}{5}$
• B. $\frac{3}{4}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

The correct option is C $\frac{1}{4}$

$n\left(S\right)=$ area of circle with radius $R=\pi R^2$
$n\left(A\right)=$ area of circle with radius $\frac{R}{2}=\frac{\pi R^2}{4}$
$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{\pi R^2}{\left(\pi R^2\right)\times 4}=\frac{1}{4}$