An experiment consists of selecting a point $(x, y)$ from the interior of the unit circle, $x^2 + y^2 < 1$. (a) What fraction of the points in the space satisfy $x > \frac{1}{2}$? (b) What fraction of the points in the space satisfy $x^2 + y^2 > \frac{1}{2}$? (c) What fraction of the points in the space satisfy $x + y > \frac{1}{2}$? (d) What fraction of the points in the space satisfy $x + y = \frac{1}{2}$?
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To visualize this, let's consider the unit circle centered at the origin. The line x + y = 0 is the line that passes through the origin and has a slope of -1. Now, let's think about the region of the unit circle that lies above this line. This region is the Show more…
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