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# probability

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A point P is randomly selected from the square region with vertices at $(\pm 2, \pm 2)$. What is the probability that is within one unit of (2,2)? Express your answer as a common fraction in terms of pi.

Apr 5, 2021

#1
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The square with vertices at $(\pm2, \pm2)$ has area $4*4=16$.

A circle that is one unit from $(2,2)$ has area $1*\pi$.

But wait! Only a quarter of that circle is in the square so the final probability is $\frac{\frac{\pi}{4}}{16}=\boxed{\frac{\pi}{64}}$

A graph is shown here: https://www.desmos.com/calculator/g21hwkcyzd

Apr 5, 2021
edited by RiemannIntegralzzz  Apr 5, 2021
#2
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Consider the circle centered at $(2,2)$ with radius $1$. P must lie in this circle, inside the square. This is a quarter of the circle, which you can find the area of. Then find the area of the square and use geometric probability principle.

Apr 5, 2021