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# Probability

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Two real numbers are chosen at random between 0 and 2. What is the probability that the sum of their squares is no more than 3? Express your answer as a common fraction in terms of pi.

Jul 4, 2022

#1
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The area of the sucsesses is a quarter of a circle with a radius of $$\sqrt 3$$, so the area is $$\pi \sqrt{3}^2 \times {1 \over 4} = {3 \over 4} \pi$$

The area of the total region is $$2 \times 2 = 4$$

So, the probability is $${{{3 \over 4} \pi }\over 4 } = \color{brown}\boxed{3 \pi \over 16}$$

Here is an image:

Jul 4, 2022

#1
+2448
0

The area of the sucsesses is a quarter of a circle with a radius of $$\sqrt 3$$, so the area is $$\pi \sqrt{3}^2 \times {1 \over 4} = {3 \over 4} \pi$$

The area of the total region is $$2 \times 2 = 4$$

So, the probability is $${{{3 \over 4} \pi }\over 4 } = \color{brown}\boxed{3 \pi \over 16}$$

Here is an image:

BuilderBoi Jul 4, 2022