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# Probability

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A point P is randomly selected from the square region with vertices at $(\pm 1, \pm 1)$. What is the probability that P is within one unit of the origin? Express your answer as a common fraction in terms of pi.

Dec 21, 2021

#1
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The locus of points with distance 1 from the origin form a circle with center (0,0), since all of these distances are the circle's radii. Notice that the circle fits inside the square; the square's center is (0,0), and the maximum of the circle, or (0,1), is on the square. The area of the square is 2 * 2 = 4, and the area of the circle is 1^2 * π = π. So, the probability is π/4.

See https://web2.0calc.com/questions/help_73083 for further clarification.

Dec 21, 2021
#2
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Area of square   2 x 2 = 4 units2

Area of circle      pi (12) = pi   units2

What is the probability that P is within one unit of the origin?     pi / 4

Dec 21, 2021