A point is randomly chosen inside a square of side length 2. What is the probability that the distance between the chosen point and the nearest corner of the square is between 1/2 and 1?
We can consider just a 1 x 1 square and two circles with equations x^2 + y^2 =1 and x^2 + y^2 = 1/4
The area of the smal square= 1
The area between the circles is (1/4) pi ( 1^2 - (1/2)^2) = (3/4)pi / 4 = (3/16) pi
The probability is (3/16)pI / 1 ≈ .589 ≈ 58.9%
What would be the fractional answer though?
3pi / 16
