Note that the area of the red region is just the area of the larger circle - area of the smaler circle =
(8.01^2 - 4.02^2) pi
So.....the probability that a point fals into the red area =
red area / area of large circle =
(8.01^2 - 4.02^2) pi 8.01^2 - 4.02^2
________________ = ______________ ≈ .748 = 74.8 %
8.01^2 pi 8.01^2