A point is selected randomly from the interior of the circle,the probability that it is closer to boundary rather than the centre of the circle is ?

Hello student,

Dividing the circle of radius r, into two parts with a smaller circle of radius r/2 and the remaining portion between the smaller circle and the larger one.
The smaller circle has an area of Pi *(r/2)^2 and the remaining region with an area Pi*r^2 - Pi *(r/2)^2.
The point that lies in this region is more closer to the circumference than the center.So, P = (Pi*r^2 - Pi *(r/2)^2)/ (Pi*r^2) =3/4

Thanks and Regards

Shaik Aasif

askIITians faculty