To: Solveit:
I copied your very interesting question of this morning, about faculty, just a few questions below this one. I posted my answer to it. Please look at it. Sometimes simple logic in concrete words and numbers is a much better solution than abstract symblic Algebra. Thanks.
+129852 Call the radius of the circle, r.
The area of the surrounding square, ABCD = 4r^2
The area of the square inscribed in the circle = 2r^2
The area of the circle = pi*r^2
So.....the shaded area = the area of the circle - the area of the inscribed square = [pi*r^2 -2r^2]
So....the probability that a point is chosen in the shaded area =
shaded area / total area bounded by ABCD =
[pi *r^2 - 2r^2] / [4r^2] =
r^2 [ pi - 2]/ {r^2 *4] = [ r^2 cancels ]
[pi - 2 ] / 4 (E)
