By the larger circle, they mean the red area plus the white area. We now must calculate the area of both.
Small circle area (white area)= PI * 4.02^2 = 50.77 square inches
TOTAL Circle Area (red and white) = PI * 8.01 *8.01 = 201.56
(Red area)= PI * 8.01^2 -50.77
(Red area)= 201.56 -50.77 = 150.79
A point chosen in the TOTAL 201.5648988136 square inch area has the probability of being in the read area=
red area / TOTAL area = 150.79 / 201.56
probability = .748 = 74.8% of the time.