2022-09-24

Geometric Probability. Sphere
Suppose a sphere with radius R. Find the probability of the event such that n selected points of the sphere are within the distance of $r=\frac{R}{2}$ from the center of the sphere. The points are uniformly distributed and selected independently.

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Zackary Galloway

Expert

Explanation:
Since the points are independent and the final condition doesn't correlate them in any way, each point can be treated independently so your answer of $\frac{1}{{8}^{n}}$ is correct.

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