This answer is approximate. The value is rounded to the nearest tenth of a percent.
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Explanation:
Let, X = area of the larger circle Y = area of the smaller circle Z = area of the shaded region = X - Y
The goal is to compute the ratio Z/X to get the answer we want
Let's find area of the larger circle Area of circle = pi*(radius)^2 A = pi*r^2 X = pi*8.01^2 X = 64.1601pi This is the exact area in terms of pi
Now repeat for the smaller circle A = pi*r^2 Y = pi*4.02^2 Y = 16.1604pi
Subtract those results to find the value of Z Z = X-Y Z = 64.1601pi-16.1604pi Z = 47.9997pi This is the exact area of the red donut region
Divide Z over X to get the probability of landing in the red region Z/X = (47.9997pi)/(64.1601pi) Z/X = (47.9997)/(64.1601) <--- note how the pi terms cancel Z/X = 0.74812 which is approximate
Convert to a percent Move the decimal point 2 spots to the right 0.74812 ---> 74.812%
Then round this to one decimal place 74.812% ---> 74.8%
