Solution

Probability of point lying close to circumference would be mean point is in the circle with area from r/2 from center till outside in the figure below it would be in blue part of the circle.

Probability = Area covered by circle from point r/2 towards circumference/ Area of the circle

In the above given circle formula would be = Area of blue circle/ Area of circle

= pi r pow 2/ 4 / pi r 2 = 1/4