SOLUTION: A shaded circle is inside a square with one side of the square measuring 2" and the bottom side of the square measuring 2". FIND THE PROBABILITY THAT AN OBJECT LANDING RANDOMLY ON

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Question 275115: A shaded circle is inside a square with one side of the square measuring 2" and the bottom side of the square measuring 2". FIND THE PROBABILITY THAT AN OBJECT LANDING RANDOMLY ON THE FIGURE WILL LAND IN THE SHADED CIRCLE. " EXPRESS THE PROBABILITY AS A PERCENT.
Answer by Earlsdon(6294) About Me  (Show Source):
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The probability P(c) of the object landing in the shaded circle is given by the ratio of the area of the shaded circle A%5Bc%5D to the area of the square A%5Bsq%5D:
We are of course assuming that the sides of the square are tangent to (just touching) the circumference of the shaded circle, in which case, the diameter (D) of the shaded circle is equal to the length (S) of the side of the square, or 2".
P%28c%29+=+A%5Bc%5D%2FA%5Bsq%5D
P%5Bc%5D+=+%28%28pi%29%28D%2F2%29%5E2%29%2F%28S%5E2%29 Substitute: D = 2, pi+=+3.14, and S = 2.
P%5Bc%5D+=+%283.14%282%2F2%29%5E2%29%2F%282%5E2%29 Evaluate.
P%5Bc%5D+=+3.14%2F4
P%5Bc%5D+=+78.54%